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Look up disjoint in Wiktionary, the free dictionary. Disjoint may refer to: Disjoint sets, sets with no common elements Mutual exclusivity, the impossibility...

formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the...

In mathematics, the disjoint union (or discriminated union) A ⊔ B {\displaystyle A\sqcup B} of the sets A and B is the set formed from the elements of...

almost disjoint if their intersection is small in some sense; different definitions of "small" will result in different definitions of "almost disjoint". The...

mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is analogous to the disjoint union of sets...

a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping)...

analysis, two elements x and y of a vector lattice X are lattice disjoint or simply disjoint if inf { | x | , | y | } = 0 {\displaystyle \inf \left\{|x|,|y|\right\}=0}...

equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, in the disjoint union the...

field extension Ω {\displaystyle \Omega } of k are said to be linearly disjoint over k if the following equivalent conditions are met: (i) The map A ⊗...

called edge-disjoint or simply disjoint cycle cover. Similar definitions exist for digraphs, in terms of directed cycles. Finding a vertex-disjoint cycle cover...

network routing, Suurballe's algorithm is an algorithm for finding two disjoint paths in a nonnegatively-weighted directed graph, so that both paths connect...

mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general...

In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space. There are several rather similar...

structures has the strong amalgamation property (SAP), also called the disjoint amalgamation property (DAP), if for every amalgam with A,B,C ∈ K there...

topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological...

hull of 25 disjoint 24-cells. Each 24-cell is the convex hull of 3 disjoint (8-point) 16-cells, so the 120-cell is the convex hull of 75 disjoint 16-cells...

partition the elements of X (or a subset of them) into a set of pairwise-disjoint pairs. Under certain conditions, a player can win using the following greedy...

separation axioms are about the use of topological means to distinguish disjoint sets and distinct points. It's not enough for elements of a topological...

laminar set family is a set family in which each pair of sets are either disjoint or related by containment. Formally, a set family F = { S 1 , S 2 , … }...

graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices. Proved by Karl Menger...

In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes...

largest open set disjoint from S , {\displaystyle S,} namely, it is the union of all open sets in X {\displaystyle X} that are disjoint from S . {\displaystyle...

disjoint, while the set of even numbers intersects the set of multiples of 3 at the multiples of 6. two parallel lines in the same plane are disjoint...

have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. In this case, the set of the cycles constitutes...

Fuzzy sets are disjoint if and only if their supports are disjoint according to the standard definition for crisp sets. For disjoint fuzzy sets A , B...

The 600-cell can be partitioned into five disjoint 24-cells (10 different ways), and also into 24 disjoint pentagons (inscribed in the 12 Clifford parallel...

characteristic of their disjoint union is the sum of their Euler characteristics, since homology is additive under disjoint union: χ ( M ⊔ N ) = χ (...

separated. A most basic way in which two sets can be separated is if they are disjoint, that is, if their intersection is the empty set. This property has nothing...

that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function. Urysohn's lemma...

want the size of the union of disjoint sets to be the sum of their individual sizes, even for an infinite sequence of disjoint sets. One would like to assign...

Now obtain M 1 # M 2 {\displaystyle M_{1}\mathbin {\#} M_{2}} from the disjoint sum ( M 1 − i 1 ( 0 ) ) ⊔ ( M 2 − i 2 ( 0 ) ) {\displaystyle (M_{1}-i_{1}(0))\sqcup...

unions of pairwise disjoint sets: if A 1 , A 2 , A 3 , … {\displaystyle A_{1},A_{2},A_{3},\ldots } is a sequence of pairwise disjoint sets in D {\displaystyle...

distinct in the disjoint union. This is obtained by labelling the elements by the indexes of the set they are coming from. The disjoint union of two sets...

mathematical logic, Lusin's separation theorem states that if A and B are disjoint analytic subsets of Polish space, then there is a Borel set C in the space...

graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint...

to cover, up to a Lebesgue-negligible set, a given subset E of Rd by a disjoint family extracted from a Vitali covering of E. There are two basic versions...

or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and...

into non-disjoint and disjoint by the shape of their two non-bonding molecular orbitals (NBMOs). Both NBMOs of molecules with non-disjoint characteristics...

of matroid, describing sets of vertices that can be reached by vertex-disjoint paths in a directed graph. The concept of a gammoid was introduced and...

_{i}<\prod _{i\in I}\lambda _{i}.} The sum here is the cardinality of the disjoint union of the sets, and the product is the cardinality of the Cartesian...

dividing an entire space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning...

to the disjoint-set data structure. Thus, Tarjan and La Poutré used this model to prove lower bounds on the amortized complexity of a disjoint-set data...

{ E k } k = 1 ∞ {\displaystyle \{E_{k}\}_{k=1}^{\infty }} of pairwise disjoint sets in Σ {\displaystyle \Sigma } , μ ( ⋃ k = 1 ∞ E k ) = ∑ k = 1 ∞ μ (...

force a draw. It is based on dividing the positions on the game-board into disjoint pairs. Whenever the opponent picks a position in a pair, the player picks...

Alspach's conjecture is a mathematical theorem that characterizes the disjoint cycle covers of complete graphs with prescribed cycle lengths. It is named...

edge-independent (or edge-disjoint) if they do not have any edge in common. Two internally disjoint paths are edge-disjoint, but the converse is not necessarily...

Equals, Contains, Covers, CoveredBy, Intersects, Within Anti-reflexive: Disjoint Symmetric: Equals, Intersects, Crosses, Touches, Overlaps Transitive: Equals...

extension to disconnected graphs would require that the graph is not a disjoint union of C3. More generally, a graph G is said to be a line perfect graph...

mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, μ ( A ∪ B ) =...

space is a sub-Stonean space, i.e., any two open σ-compact disjoint subsets have disjoint compact closures. Corona theorem Corona algebra, a non-commutative...

1 n C i {\displaystyle A\setminus B=\bigcup _{i=1}^{n}C_{i}} for some disjoint C 1 , … , C n ∈ S . {\displaystyle C_{1},\ldots ,C_{n}\in {\mathcal {S}}...

{\displaystyle A\star B} , is a topological space formed by taking the disjoint union of the two spaces, and attaching line segments joining every point...

the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element). More formally, given...

{\displaystyle n} -dimensional doubly directed hypercube graph be routed with edge-disjoint paths? More unsolved problems in mathematics In mathematics, Szymanski's...

points have disjoint neighbourhoods. T2 spaces are always T1. T2½ or Urysohn. A space is Urysohn if every two distinct points have disjoint closed neighbourhoods...

other two radii) covers all three eigenvalues. If one of the discs is disjoint from the others then it contains exactly one eigenvalue. If however it...

σ-compact. A manifold need not be connected, but every manifold M is a disjoint union of connected manifolds. These are just the connected components of...

subgroup H of a group G may be used to decompose the underlying set of G into disjoint, equal-size subsets called cosets. There are left cosets and right cosets...

actions. In mathematical terms, the addition principle states that, for disjoint sets A and B, we have | A ∪ B | = | A | + | B | {\displaystyle |A\cup B|=|A|+|B|}...

E ) {\displaystyle G=(V,E)} is a partition of V {\displaystyle V} into disjoint sets V 1 {\displaystyle V_{1}} , V 2 {\displaystyle V_{2}} ,..., V K {\displaystyle...

or separated space, is a topological space where distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a...

_{k=1}^{\infty }E_{k}} (up to a set of measure zero), and these sets are disjoint. Therefore: ∫ A n A ( x ) d μ ( x ) = ∑ k = 1 ∞ k ⋅ μ ( E k ) {\displaystyle...

phrasal categories including tense, aspect, negation, mood and the conjoint/disjoint paradigm. Dawuni Dawuni kú-r-í kill-IPFV-CONJ sòònsí rabbits máá. DEF Dawuni...

In set theory, an amorphous set is an infinite set that is not the disjoint union of two infinite subsets. Amorphous sets cannot exist if the axiom of...

remote city and worked in his spare time on the problem of large sets of disjoint Steiner triple systems. Lu Jiaxi was born in a poor family in Shanghai...

particularly strong form: any closed subset of X can be written uniquely as the disjoint union of a perfect set and a countable set. In particular, every uncountable...

describes how many edge-disjoint spanning trees (and more generally forests) a graph can have: A graph G has t edge-disjoint spanning trees iff for every...

operations : Creation of a new vertex v with label i (denoted by i(v)) Disjoint union of two labeled graphs G and H (denoted by G ⊕ H {\displaystyle G\oplus...

E_{1})} and G 2 = ( V 2 , E 2 ) {\displaystyle G_{2}=(V_{2},E_{2})} be two disjoint graphs. The join G 1 + G 2 {\displaystyle G_{1}+G_{2}} is a graph with:...

the κ {\displaystyle \kappa } -hedgehog space is formed by taking the disjoint union of κ {\displaystyle \kappa } real unit intervals identified at the...

and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K1 and is closed under complementation and disjoint union...

limits. The dual notion of a colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits. Limits and...

of Z 3 4 {\displaystyle \mathbb {Z} _{3}^{4}} can be partitioned into disjoint cap sets. They reported that it is possible to use four different cap sets...

\dots } must all be mutually disjoint. Because T {\displaystyle T} is a measure-preserving transformation, all of these disjoint sets must have the exact...

cyclic permutations, but every permutation can be written as a product of disjoint (having no common element) cycles in essentially one way. As a permutation...

Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each...

form a cycle. The key steps of the algorithm are sorting and the use of a disjoint-set data structure to detect cycles. Its running time is dominated by the...

a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher. The boundary...

two parameters of a graph: The size of the largest collection of vertex-disjoint cycles contained in the graph; The size of the smallest feedback vertex...

includes at least one edge from each dicut. If a collection of dicuts are all disjoint, any dijoin must have at least one edge from each of these dicuts, and...

}}y} in a vector lattice X {\displaystyle X} are said to be lattice disjoint or disjoint if inf { | x | , | y | } = 0 , {\displaystyle \inf\{|x|,|y|\}=0,}...

theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: ∀ x ( x ≠ ∅ → ( ∃ y ∈ x...

be written as the union of two proper closed subsets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry...

pairwise almost disjoint. A maximal almost disjoint ("mad") family of subsets of ω {\displaystyle \omega } is thus an almost disjoint family A {\displaystyle...

p. If a continuum is indecomposable, then its composants are pairwise disjoint. The composants of a continuum are dense in that continuum. Solecki, Sławomir...

theory with the Axiom of Choice (ZFC). This is because one can find two disjoint stationary sets, which precludes the filter from deciding membership for...

significant position first. Effectively, each element of T is replaced by a disjoint copy of S. The order-type of the Cartesian product is the ordinal that...

length two are transpositions. Two cycles are disjoint if they have disjoint subsets of elements. Disjoint cycles commute: for example, in S6 there is the...

require that every ideal that is disjoint from a given filter can be extended to a prime ideal that is still disjoint from that filter. In the case of...

one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A directed tree, oriented tree, polytree, or singly connected...

a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching in a graph. Recall that a...

states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree. Thus, it is...

two definitions. In the most common one, the disjoint union of graphs, the union is assumed to be disjoint. Less commonly (though more consistent with...

\nu (G)} is the "triangle packing number", the largest number of edge-disjoint triangles that it is possible to find in G {\displaystyle G} . It can be...

\left(\textstyle \bigcup \limits _{i=1}^{n}F_{i}\right)} for all pairwise disjoint finite sequences F 1 , … , F n ∈ F {\displaystyle F_{1},\ldots ,F_{n}\in...

portions, using a carving knife or meat-slicing machine. A meat carver disjoints the meat and slices in uniform portions. Meat carving is sometimes considered...

tangent vectors at each point in the manifold can be classified into three disjoint types. A tangent vector X {\displaystyle X} is: timelike if g ( X , X )...

two vertices are adjacent if and only if the two corresponding sets are disjoint. Kneser graphs are named after Martin Kneser, who first investigated them...

subset has a supremum and an infimum; and every collection of mutually disjoint non-empty open intervals in R is countable (this is the countable chain...

least two disjoint intervals; The union of the vertical segments (yi, yi+hi), over all i in E(i1,i2,j1,j2), is made up of at least two disjoint intervals...

subset of a topological space that cannot be covered by the union of two disjoint non-empty open sets Connected-component labeling, an algorithm for finding...

edges in a dicut of a directed graph always equal the maximum number of disjoint dijoins? More unsolved problems in mathematics In the mathematics of directed...

space, there exists a decomposition of the ball into a finite number of disjoint subsets that can be put back together in a different way to yield two identical...

Mexico, where the Hawikuh Ruins are located The Cibola National Forest, a disjoint forest stretching from New Mexico to Oklahoma, including parts of Cibola...

𝜆-system (Dynkin system) – Family closed under complements and countable disjoint unions List of Boolean algebra topics Measure theory – Generalization of...

A r i t y ( S ) {\displaystyle \mathrm {Arity} (S)} -indexed family of disjoint sets of operators. If o {\displaystyle o} is an operator arity ( s 1 ,...

In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated"...

endpoints in question. Intuitively, this corresponds to a space that has no disjoint parts and no holes that go completely through it, because two paths going...

that are not members of the set. Curves which do not overlap represent disjoint sets, which have no elements in common. Two curves that overlap represent...

permutation can be expressed as the product of disjoint cycles (more precisely: cycles with disjoint orbits); such cycles commute with each other, and...

{\displaystyle L\cap R\neq \varnothing .} Sets that do not intersect are said to be disjoint. The power set of X {\displaystyle X} is the set of all subsets of X {\displaystyle...

width). In formal terms, these variants are known as tagged unions or disjoint unions. Each variant has a name, called a constructor, which can also carry...

occurs if and only if A {\displaystyle A} and B {\displaystyle B} are disjoint sets. Furthermore, denoting D = A Δ B {\displaystyle D=A\mathbin {\Delta...

degrees on each axis. The problem of finding the smallest ball such that k disjoint open unit balls may be packed inside it has a simple and complete answer...

is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane. The two-component unlink, consisting of two non-interlinked...

exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only...

) of X {\displaystyle X} by G {\displaystyle G} are pairwise disjoint (meaning, disjoint from X {\displaystyle X} and from each other). The set of those...

A\subseteq B} only if A i ↗ {\displaystyle A_{i}\nearrow } or they are disjoint Never Ring (order theory) Ring (measure theory) Never δ-ring Never 𝜎-ring...

forest is a kind of forest where each component is a path graph, or a disjoint union of nontrivial paths. Equivalently, it is an acyclic and claw-free...

disjoint, each element of the transversal corresponds to exactly one member of C (the set it is a member of). If the original sets are not disjoint,...

Maryland Northwestern University Thesis Efficient Parallel Algorithms for Disjoint Paths and Connectivity (1990) Doctoral advisor Vijay Vazirani Other academic...

In mathematics, the lakes of Wada (和田の湖, Wada no mizuumi) are three disjoint connected open sets of the plane or open unit square with the counterintuitive...

Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S 1 {\displaystyle S^{1}} -bundle...

additivity property says that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities...

subsets, then it is vacuously a sunflower. If W {\displaystyle W} contains disjoint subsets, then it is a sunflower, with an empty kernel. The study of sunflowers...

for K in H, so H = ⨆ s ∈ S s K {\displaystyle H=\bigsqcup _{s\in S}sK} (disjoint union), and | S | = [ H : K ] {\displaystyle |S|=[H:K]} . For any a ∈ G...

also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin...

{\displaystyle X} and the elements of X {\displaystyle X} are pairwise disjoint, then there exists a set C {\displaystyle C} such that its intersection...

also called a variant, variant record, choice type, discriminated union, disjoint union, sum type, or coproduct, is a data structure used to hold a value...

topological space – a topological space in which every two disjoint closed sets have disjoint open neighborhoods Paracompact space – Topological space which...

University IBM Almaden Research Center Thesis Approximation algorithms for disjoint paths problems (1996) Doctoral advisor Michel Goemans Website videolectures...

Edmonds and Karp, as well as in Suurballe's algorithm for finding two disjoint paths of minimum total length between the same two vertices in a graph...

space has a countable subfamily which is still a base. Every collection of disjoint open sets in a second-countable space is countable. A metric space that...

S\rangle ,} meaning that there is a copy of the full integers that lies disjoint from the original copy of the natural numbers within this model; in this...

(sometimes also written as X + f Y {\displaystyle X+_{f}Y} ) by taking the disjoint union of X {\displaystyle X} and Y {\displaystyle Y} and identifying a...

connected. disjoint 1.  Two subgraphs are edge disjoint if they share no edges, and vertex disjoint if they share no vertices. 2.  The disjoint union of...

each. Each independent set is disjoint from exactly 7 other independent sets. The 100-vertex graph that connects disjoint independent sets can be partitioned...

into parallel classes which are themselves partitions of the points into disjoint blocks. Such Steiner systems that have a parallelism are also called resolvable...

iff there are k {\displaystyle k} edge-disjoint paths. 2. The paths must be independent, i.e., vertex-disjoint (except for s {\displaystyle s} and t {\displaystyle...

{\displaystyle \delta =o(b)} bits). In the disjoint-set data structure, the structure represents a collection of disjoint sets; there is an update operation,...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

{\displaystyle Y} , the fiber f − 1 ( y ) {\displaystyle f^{-1}(y)} is the disjoint union of points, each of which is the spectrum of a finite separable field...

successive displacements are random, in which displacements in pairwise disjoint time intervals are independent, and displacements in different time intervals...

theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs. Equivalently, a graph is a cluster graph if and...

single connected component. An undirected graph can be decomposed into edge-disjoint cycles if and only if all of its vertices have even degree. So, a graph...

uniquely characterize this space up to homeomorphism. For example, the disjoint union of a Sierpiński carpet and a circle is also a universal plane curve...

if and only if it contains its boundary, and open if and only if it is disjoint from its boundary. The closure of a set S {\displaystyle S} equals the...

of length 0 (a single vertex). A path cover may also refer to a vertex-disjoint path cover, i.e., a set of paths such that every vertex v ∈ V belongs to...

2020-10-24. Retrieved 2020-10-21. Roskind, James Anthony (1983). Edge disjoint spanning trees and failure recovery in data communication networks (PhD...

as the disjoint union of a perfect set and a countable set. Moreover, if X {\displaystyle X} is uncountable, it can be written as the disjoint union of...

the ordering. A line graph is a graph whose edges can be covered by edge-disjoint cliques in such a way that each vertex belongs to exactly two of the cliques...

β } β < λ {\displaystyle \{A_{\beta }\}_{\beta <\lambda }} of pairwise disjoint subsets A β ⊆ κ {\displaystyle A_{\beta }\subseteq \kappa } , we have μ...

subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization...

F such that I is disjoint from F. We are interested in an ideal M that is maximal among all ideals that contain I and are disjoint from F. In the case...

e., the subsets in S ∗ {\displaystyle {\mathcal {S}}^{*}} are pairwise disjoint. In other words, each element in X {\displaystyle X} is contained in at...

In mathematics, a separoid is a binary relation between disjoint sets which is stable as an ideal in the canonical order induced by inclusion. Many mathematical...

In cooking, this knife was originally designed primarily to slice and disjoint large cuts of beef and mutton, though now it is the primary general food...

assumed to have the following two properties: The intervals are pairwise disjoint: A i ∩ A j = ∅ {\displaystyle A_{i}\cap A_{j}=\emptyset } for i ≠ j {\displaystyle...

connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself...

locally compact Hausdorff space such that any two open σ-compact disjoint subsets have disjoint compact closures. Related, an F-space, introduced by Gillman...

{\displaystyle \{A\}} (constructed using pairing) necessarily contains an element disjoint from { A } {\displaystyle \{A\}} , by regularity. Because its only element...

finite collection of progressions has the property that no two of them are disjoint, then there exists an integer that belongs to all of them; this is the...

"SupplementalArrowsA" and "SUPPLEMENTALARROWSA". Blocks are pairwise disjoint; that is, they do not overlap. The starting code point and the size (number...

min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric. In the simplest unweighted min-cut...

{\displaystyle [y]} are either equal if x ∼ y {\displaystyle x\sim y} , or disjoint otherwise. Therefore, the set of all equivalence classes of X {\displaystyle...

A\subseteq B} only if A i ↗ {\displaystyle A_{i}\nearrow } or they are disjoint Never Ring (order theory) Ring (measure theory) Never δ-ring Never 𝜎-ring...

vector space of dimension n or more generally a matroid of rank n, with n disjoint bases Bi, then it is possible to arrange the elements of these bases into...

points. Local connectedness does not imply connectedness (consider two disjoint open intervals in R {\displaystyle \mathbb {R} } for example); and connectedness...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

deity or other divine being. Depending on the religion, these might be disjoint or overlapping parts, or methods of perceiving or conceptualizing the deity...

theory) states that for any two disjoint analytic subsets of a Polish space there is a Borel subset containing one but disjoint from the other. Hyperplane...

matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates"). The matching is stable if there are no two elements...

preprocessing O ~ ( n + 2 d ) {\displaystyle {\tilde {O}}(n+2^{d})} Precompute disjointness structure d = c log ⁡ n {\displaystyle d=c\log n} , for all constants...

people (2010). The surrounding area, Bugac puszta is the largest of seven disjoint units making up the Kiskunság National Park. Bugac was founded by the local...

each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane...

real algebraic numbers. So both T and R are the union of three pairwise disjoint sets: T0 and two countable sets. A one-to-one correspondence between T...

computationally whether a graph is connected (for example, by using a disjoint-set data structure), or to count the number of connected components. A...

paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest. Paths are fundamental concepts...

instance, this is true for the following problems: Finding the largest disjoint subset of a collection of unit disks in the hyperbolic plane can be solved...

S can be divided up into 2g − 2 pairs of pants by cutting along 3g − 3 disjoint simple closed curves. For each of these 3g − 3 curves γ, choose an arc...

{\displaystyle A_{1},A_{2},A_{3},\ldots } is a sequence of (pairwise) disjoint subsets in D {\displaystyle D} then ⋃ n = 1 ∞ A n ∈ D . {\displaystyle...

any open set is a disjoint union of sets in it. Compare this with base in topology, which is less restrictive as it allows non-disjoint unions. Knopp's...

given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely...

A chain decomposition is a partition of the elements of the order into disjoint chains. Dilworth's theorem states that, in any finite partially ordered...

the matroid whose underlying set is the disjoint union of E and F, and whose independent sets are the disjoint unions of an independent set of M with an...

A of an abelian group G is said to be sum-free if the sumset A + A is disjoint from A. In other words, A is sum-free if the equation a + b = c {\displaystyle...

D_{x}} such that π − 1 ( U x ) {\displaystyle \pi ^{-1}(U_{x})} is the disjoint union ⨆ d ∈ D x V d {\displaystyle \displaystyle \bigsqcup _{d\in D_{x}}V_{d}}...

divisor of all the terms gcd {\displaystyle \gcd } Category theory Coproduct Disjoint union Coproduct of objects ∐ {\displaystyle \coprod } Product Cartesian...

members of X. Open balls of radius r centered at the points of X will all be disjoint from each other. The covering radius, R, of X is the smallest distance...

cellular decomposition G of a manifold M is a decomposition of M as the disjoint union of cells (spaces homeomorphic to n-balls Bn). The quotient space...

space is a partition of its points into disjoint lines, and a packing is a partition of the lines into disjoint spreads. In PG(3,2), a spread would be...

whether the circles cross each other, are tangent to each other, or are disjoint from each other. The inversive distance remains unchanged if the circles...

_{n=1}^{\infty }A_{n}\right)=\sum _{n=1}^{\infty }\mu _{0}(A_{n})} for any disjoint family { A n : n ∈ N } {\displaystyle \{A_{n}:n\in \mathbb {N} \}} of elements...

Then E is an open set, and it may be written as a countable union of disjoint intervals E = ⋃ k ( a k , b k ) {\displaystyle E=\bigcup _{k}(a_{k},b_{k})}...

discrete topology). A 1-dimensional CW complex is constructed by taking the disjoint union of a 0-dimensional CW complex with one or more copies of the unit...

enable more local execution of graph queries ("Hybrid SmartGraphs", "Hybrid Disjoint SmartGraphs"). Language-agnostic tokenization of text ("Segmentation Analyzer")...

of 2. In a complete bipartite graph, the vertex set is the union of two disjoint sets, W and X, so that every vertex in W is adjacent to every vertex in...

P {\displaystyle P} . So P {\displaystyle P} must form a collection of disjoint cycles, of paths with an equal number of matched and unmatched edges in...

given by the cartesian product of sets. The coproduct is given by the disjoint union: given sets Ai where i ranges over some index set I, we construct...

specific tracker while being unable to connect to another. This can create a disjoint set which can impede the efficiency of a torrent to transfer the files...

edge-disjoint paths connecting them. (Every vertex is related to itself via two length-zero paths, which are identical but nevertheless edge-disjoint.) The...

the probability that both w>x and y>z. There are even distributions with disjoint supports, which induce the same set of choice probabilities. Some conditions...

torus in an interesting way) or Seifert-fibered (can be decomposed into a disjoint union of circles in a nice way). The statement of the JSJ decomposition...

another dense subset which shows that a topological space may have several disjoint dense subsets (in particular, two dense subsets may be each other's complements)...

partition V into k parts (subsets) V1, V2, ..., Vk such that the parts are disjoint and have equal size, and the number of edges with endpoints in different...

simple rule of disjoint reference (which stipulated that any pronoun following a noun phrase (NP) antecedent in the same sentence has disjoint reference with...

cone) and an arbitrary subset A (the basis) of some other subspace S, disjoint from R. In the special case that R is a single point, S is a plane, and...

S_{\operatorname {func} }} and S rel {\displaystyle S_{\operatorname {rel} }} are disjoint sets not containing any other basic logical symbols, called respectively...

{\displaystyle {\mathcal {S}}} and F {\displaystyle {\mathcal {F}}} are disjoint, and H {\displaystyle {\mathcal {H}}} are the minimal graphs in C {\displaystyle...

and if any two disjoint closed subsets of X are separated by neighbourhoods. (In fact, a space is normal if and only if any two disjoint closed sets can...

assumption on the domain D is necessary. For example, if D consists of two disjoint open sets, f {\displaystyle f} can be 0 {\displaystyle 0} on one open set...

Unsolved problem in mathematics For how many points is it always possible to projectively transform the points into convex position? More unsolved problems...

at all times of day. If the number of calls received in any two given disjoint time intervals is independent, then the number k of calls received during...

, B 2 , B 3 , … {\displaystyle B_{1},B_{2},B_{3},\dots } are pairwise disjoint events, then P ( ⋃ i B i ) = ∑ i P ( B i ) . {\displaystyle \mathbb {P}...

a single contiguous piece, we give each partner a union of one or more disjoint pieces. The general scheme is as follows: Each partner privately partitions...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

time are mutually disjoint, and then one defines the Jordan measure m ( S ) {\displaystyle m(S)} as the sum of measures of the disjoint rectangles. One...

function is a set function whose value when applied to the union of two disjoint sets is greater than or equal to the sum of values of the function applied...

2) is a partition of points into disjoint lines, and corresponds to the arrangement of girls (points) into disjoint rows (lines of a spread) for a single...

projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The...

K and L such as K= Card(A) and L = Card(B) where the sets A and B are disjoint, is Card (A ∪ B). The definition of a finite set is given independently...

from ⁠ f ( i ) {\displaystyle f(i)} ⁠. By the Hausdorff condition, choose disjoint open sets V {\displaystyle V} and W {\displaystyle W} that contain y {\displaystyle...

tangent vectors in M {\displaystyle M} . As a set, it is given by the disjoint union of the tangent spaces of M {\displaystyle M} . That is, T M = ⨆ x...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

This group R / Q {\displaystyle \mathbb {R} /\mathbb {Q} } consists of disjoint "shifted copies" of Q {\displaystyle \mathbb {Q} } in the sense that each...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

groups. That is, the free product plays the same role in group theory that disjoint union plays in set theory, or that the direct sum plays in module theory...

base for the space is generally not a filter base since it may contain disjoint sets, but the subset of a base consisting of all sets containing some given...

possible. Bierlein's extension theorem says, that it is always possible for disjoint families. Bierlein's measure extension theorem is Let ( X , A , μ ) {\displaystyle...

attributed to Julius König. Assume without loss of generality that A and B are disjoint. For any a in A or b in B we can form a unique two-sided sequence of elements...

the set of balls of radius s centered at each codeword of C are mutually disjoint. From the proof of the Hamming bound, it can be seen that for t = ⌊ 1 2...

that do not share an axis (e.g. in the xy and wz planes) are completely disjoint (they do not intersect at any vertices). These planes are completely orthogonal...

probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set...

the result of removing from the sphere three open disks with pairwise disjoint closures. Thus a pair of pants is a compact surface of genus zero with...

{\displaystyle \delta } such that whenever a finite sequence of pairwise disjoint sub-intervals ( x k , y k ) {\displaystyle (x_{k},y_{k})} of I {\displaystyle...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Male Mahadeshwara Hills are located at the northeastern section of a disjoint projection of the Western Ghats in a northeastern direction at the southern...

λ-system (Dynkin system) – Family closed under complements and countable disjoint unions π-system – Family of sets closed under intersection Ring of sets –...

additivity: if E 1 , E 2 , … {\displaystyle E_{1},E_{2},\ldots } are pairwise disjoint measurable sets, then λ ( ⋃ k = 1 ∞ E k ) = ∑ k = 1 ∞ λ ( E k ) . {\displaystyle...

n=2^{(k+1)}-2} elements. The set system consists of k {\displaystyle k} pairwise disjoint sets S 1 , … , S k {\displaystyle S_{1},\ldots ,S_{k}} with sizes 2 , 4...

of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another...

There exists a unique solution X exactly when the spectra of A and −B are disjoint. Using the Kronecker product notation and the vectorization operator vec...

integer-perfect number where its divisors can be partitioned into two disjoint sets with equal sum. 1728 is 3-smooth, since its only distinct prime factors...

well-behaved. For instance, they may be restricted to being the closures of disjoint open sets. The Bolyai–Gerwien theorem states that any polygon may be dissected...

number triangle. A partition of a set S is a set of non-empty, pairwise disjoint subsets of S, called "parts" or "blocks", whose union is all of S. Consider...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

(isoband). Similarly, the output will contain 2 copies of the 2D vertices for disjoint lines (isoline) or 4 copies for polygons (isobands). [Under the assumptions...

metric spaces. Two related concepts are the packing number, the number of disjoint balls that fit in a space, and the metric entropy, the number of points...

that is a disjoint union of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of countably...

matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits. In a uniform matroid U n r {\displaystyle U{}_{n}^{r}} , the...

are omitted here because of their length. Open section decomposed into disjoint rectangular walls J T ≥ ∑ i 5 b i 3 t i 3 18 ( b i 2 + t i 2 ) {\displaystyle...

{\displaystyle k} or more colors, then one can find k {\displaystyle k} disjoint connected subgraphs of G {\displaystyle G} such that each subgraph is connected...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

\{A_{i}\}_{i=1}^{\infty }\subseteq {\mathcal {F}}} is a countable collection of pairwise disjoint sets, then P ( ⋃ i = 1 ∞ A i ) = ∑ i = 1 ∞ P ( A i ) , {\textstyle P(\bigcup...

in terms of the minimal area of a hypersurface that divides M into two disjoint pieces. In 1971, Jeff Cheeger proved an inequality that related the first...

under complements and countable disjoint unions π-𝜆 theorem – Family closed under complements and countable disjoint unionsPages displaying short descriptions...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

connect each vertex pair with a given number (possibly 0) of edge- or vertex-disjoint paths. The Steiner problem has also been stated in the general setting...

ethical agents and the class of patients: (1) agents and patients are disjoint, (2) patients can be a proper subset of agents, (3) agents and patients...

unlearning requests. Sharding divides the training dataset into multiple disjoint subsets, or shards. Each shard is used to train a separate model instance...

level of function fields it is possible to construct J by taking linearly disjoint copies of the function field of C, and within their compositum taking the...

{\displaystyle \mathbb {R} ^{d}} , then there are r {\displaystyle r} pairwise-disjoint faces of Δ N {\displaystyle \Delta ^{N}} whose images under f {\displaystyle...

exhibits the conjoint/disjoint alternation. The long present (with -ya-) is used when the verb appears at a phrase boundary (disjoint), while the short present...

definition.) The disjoint union of two posets is another typical example of order construction, where the order is just the (disjoint) union of the original...

problem of decomposing an Eulerian graph into a minimum number of edge-disjoint cycles is NP-complete, as is the corresponding problem of decomposing into...

equation can be deduced from the former using that, for any X that is the disjoint union of a closed and open subscheme U and V, respectively, ζ X ( s ) =...

and Y are disjoint, addition is given by the union of X and Y. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the...

sub-language of the language defined by G. Σ is a finite set of terminals, disjoint from V, which make up the actual content of the sentence. The set of terminals...

bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U {\displaystyle U} and V {\displaystyle V} , that...

{\displaystyle X} and Y {\displaystyle Y} are T {\displaystyle T} -linearly disjoint, which by definition means that for all positive integers n {\displaystyle...

derives from the action of a zipper in that it interleaves two formerly disjoint sequences. The inverse function is unzip. Given the three words cat, fish...

then A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } . Such sets are called disjoint sets and may colloquially be said to have no intersection. In geometry...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

general relativity Tetrad (geometry puzzle), a set of four simply connected disjoint planar regions in the plane Tetrad (meiosis), the four cells produced by...

geometrically as any closed balls of radius k centered on distinct codewords being disjoint. These balls are also called Hamming spheres in this context. For example...

females, there is no union, nor a tendinous perineal raphe; the parts are disjoint primarily and arise from the same central tendinous point of the perineum...

edge-disjoint paths problem, we are given an undirected graph G = (V, E) and two vertices s and t, and we have to find the maximum number of edge-disjoint...

provides an alternative and equivalent characterization, in terms of edge-disjoint paths in the graph. If and only if every two vertices of G form the endpoints...

number to be a Kaprekar number, it must belong to one of five mutually disjoint sets composed of combinations of the seven numbers 495, 6174, 36, 123456789...

{\displaystyle W_{k}(z),k\in \mathbb {Z} } are all injective and their ranges are disjoint. The range of the entire multivalued function W is the complex plane. The...

adjunctive, conjoin, conjoint, conjunct, conjunction, conjunctive, disjoin, disjoint, disjunct, disjunction, disjunctive, enjoin, enjoinder, enjoinment, injunction...

cliques of equal size, the clique-sum of G and H is formed from their disjoint union by identifying pairs of vertices in these two cliques to form a single...

algorithm finds the optimal solution to Malfatti's problem of finding three disjoint circles within a given triangle that maximize the total area of the circles;...

mathematics In combinatorics, tripod packing is a problem of finding many disjoint tripods in a three-dimensional grid, where a tripod is an infinite polycube...

generally that any two disjoint analytic sets are separated by a Borel set: in other words there is a Borel set including one and disjoint from the other. This...

and forests. (A tree is a connected graph with no cycles; a forest is a disjoint union of trees.) Gabow and Tarjan attribute the study of pseudoforests...

quite typical example: whenever a space is made up of a finite number of disjoint connected components in this way, the components will be clopen. Now let...

variable can possess. Such definitions make it possible to speak about (disjoint) unions or Cartesian products of types. Value space and behaviour A type...

two separate transition systems by building a system consisting of the disjoint union of the corresponding components. Given a labelled state transition...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

of two documents in the bags-of-words representation is, formally, the disjoint union, summing the multiplicities of each element. The BoW representation...

set is independent if and only if M {\displaystyle M} has a basis set disjoint from it. Matroid duals go back to the original paper by Hassler Whitney...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

an n {\displaystyle n} -element set, and an edge between every pair of disjoint sets. An independent set is a collection of vertices that has no edges...

train by disjoint equal rhythms from different voices. Note that the established term "rhythmic canon" is somewhat misleading, and "disjoint rhythm canon"...

algorithms. The anarboricity of a graph is the maximum number of edge-disjoint nonacyclic subgraphs into which the edges of the graph can be partitioned...

{\displaystyle (S_{12},R_{12})=(S_{1},R_{1})\bullet (S_{2},R_{2})} takes the disjoint union S 12 = S 1 ⊔ S 2 {\displaystyle S_{12}=S_{1}\sqcup S_{2}} of two...

Budan–Fourier theorem. Repeated division of an interval in two results in a set of disjoint intervals, each containing one root, and together listing all the roots...

separately, since all permutations can also be represented as products of disjoint cycles. So first let π be some k-cycle on [n]={1 ... n}. Without loss of...

set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules, each rule of the form V ∗ N...

The intersection of Cs and Ct is the set of lines on F that cuts the disjoint lines Ls and Lt. Consider the linear span of Ls and Lt: it is an hyperplane...

graphs and their complements, disjoint unions of countably infinite cliques and their complements, and infinite disjoint unions of isomorphic finite cliques...

branch of mathematics, an extension topology is a topology placed on the disjoint union of a topological space and another set. There are various types of...

property that, near almost every point, the graph of the function is the disjoint union of one or several graphs of smooth functions, which are called branches...

space is a Poisson-distributed random variable. Consider a collection of disjoint and bounded subregions of the underlying space. By definition, the number...

theory. This is the assumption of σ-additivity: Any countable sequence of disjoint events (synonymous with mutually exclusive events) E 1 , E 2 , … {\displaystyle...

path it is located in. For example, the modules A and A.B in theory are disjoint modules and need not necessarily have any relation, however employing such...

distinct points x , y ∈ X {\displaystyle x,y\in X} , there is a pair of disjoint open neighborhoods U , V {\displaystyle U,V} of x , y {\displaystyle x...

theory of algebraic number theory.) Subfields K and L of M are linearly disjoint (over a subfield N) when in this way the natural N-linear map of K ⊗ N...

The result of the θ-join is defined only if the headers of S and R are disjoint, that is, do not contain a common attribute. The simulation of this operation...

regard to disjoint unions of graphs: A graph invariant is additive if, for all two graphs G and H, the value of the invariant on the disjoint union of...

output when it is instate x and it reads letter i. This graph is a union of disjoint cycles if the automaton is bireversible[definition needed]. A simple Mealy...

property of a topological space in which it cannot be divided into two disjoint nonempty open sets. connexive logic A branch of logic that studies principles...

permutation is even or odd, one writes the permutation as a product of disjoint cycles. The permutation is odd if and only if this factorization contains...

to values. Two heaps h {\displaystyle h} and h ′ {\displaystyle h'} are disjoint (denoted h ⊥ h ′ {\displaystyle h\,\bot \,h'} ) if their domains do not...

positive ε < 1 and any δ > 0, there exists a finite sequence of pairwise disjoint sub-intervals with total length < δ over which the Cantor function cumulatively...

Houston Math. Retrieved 3 April 2022. By this definition, even a union of disjoint sets where one of these sets is an open set containing p {\displaystyle...

triangle formed by the other three. Equivalently, the lines passing through disjoint pairs among the points are perpendicular, and the four circles passing...

Y}f^{-1}[\{g(y)\}]} where ∐ {\displaystyle \coprod } is the disjoint union of sets (the involved sets are not disjoint on their own unless f resp. g is injective). In...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

{\displaystyle X} can be covered with at most countably many measurable disjoint sets with finite measure. This means that there are sets B 1 , B 2 , …...

F has bounded tree-depth if and only if its forbidden minors include a disjoint union of path graphs, F has bounded treewidth if and only if its forbidden...

secant variety) of a twisted cubic C fill up P3 and the lines are pairwise disjoint, except at points of the curve itself. In fact, the union of the tangent...

disjoint union of a perfect set and a scattered set. Cantor proved that every closed subset of the real line can be uniquely written as the disjoint union...

inclusion. That is, a condition p {\displaystyle p} is essentially two disjoint finite subsets p − 1 [ 1 ] {\displaystyle {p^{-1}}[1]} and p − 1 [ 0 ]...

E 0 {\displaystyle E_{0}} and F 0 {\displaystyle F_{0}} are closed and disjoint subsets of A {\displaystyle A} . By taking a linear combination of the...

element or maximal elements admit disjoint cofinal subsets. For example, the even and odd natural numbers form disjoint cofinal subsets of the set of all...

are order-preserving homeomorphisms between these examples. For any two disjoint total orders ( A 1 , ≤ 1 ) {\displaystyle (A_{1},\leq _{1})} and ( A 2...

{\displaystyle S} including the two distinguished vertices, as well as two disjoint subsets of the remaining unchosen edges supported on S {\displaystyle S}...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

common choices include hash tables and B-trees, other possibilities include disjoint set data structures (for storing equivalence relations), bries (a variant...

bitter enemy. The question of what the connection is between the apparently disjoint tales of Laban and Pharaoh is interpreted in several ways by rabbinical...

most Lisps, in Scheme it is #t. In Scheme the primitive datatypes are disjoint. Only one of the following predicates can be true of any Scheme object:...

set Y, where it is not the case that Y → X, and all three sets must be disjoint. A 3NF definition that is equivalent to Codd's, but expressed differently...

two disjoint dense subsets. For instance, the real numbers form a resolvable topological space because the rationals and irrationals are disjoint dense...

read an overlapping data set (e.g. values V1 and V2), concurrently make disjoint updates (e.g. T1 updates V1, T2 updates V2), and finally concurrently commit...

that is disjoint from E, then there is an ideal that is maximal among the ideals containing a 0 {\displaystyle {\mathfrak {a}}_{0}} and disjoint from E...

called mappings attached with one of the following semantic relations: disjointness (⊥), equivalence (≡), more specific (⊑) and less specific (⊒). In our...

set whose elements all are sets that are different from ∅ and mutually disjoint, its union ∪T includes at least one subset S1 having one and only one element...

{\displaystyle \Pi (U\cup V)=\max \left(\Pi (U),\Pi (V)\right)} for any disjoint subsets U {\displaystyle U} and V {\displaystyle V} . It follows that,...

Llita) who were mirror twins, being complementary diploids with entirely disjoint genomes, and thus not at increased risk for unfavorable gene duplication...

collection of circles whose union is connected and whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the...

0-handle is just a ball, and the attaching map is disjoint union. A 1-handle is attached along two disjoint 3-balls. A 2-handle is attached along a solid...

(2022), "Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions", Duke Mathematical...

1{\pmod {4}},\ 5{\pmod {6}},\ 7{\pmod {12}}\}.} A covering system is called disjoint (or exact) if no two members overlap. A covering system is called distinct...

programmer of the task of planning the moving of data between devices' disjoint memories (as must currently be done with OpenCL or CUDA). CUDA and OpenCL...

_{x\in X}{\frac {1}{|G\cdot x|}}.} Writing X {\displaystyle X} as the disjoint union of its orbits in X / G {\displaystyle X/G} gives | G | ∑ x ∈ X 1...

cycles; since distinct cycles involve disjoint sets of elements, this is referred to as "decomposition into disjoint cycles". To write down the permutation...

consists of k disjoint edges (k > 2). They proved that the number of edges of a geometric graph of n vertices, containing no 3 disjoint edges is O(n)...

topology gives a topology on the set X = R2 ⊔ {0*}, where ⊔ denotes the disjoint union. Given a point x belonging to X, such that x ≠ 0 and x ≠ 0*, the...

route markers. However, there are several numbered highways with several disjoint segments whose segments are denoted internally with letter suffixes but...

of PM) type As in type theory. All objects belong to one of a number of disjoint types. typically Relating to types; for example, "typically ambiguous"...

support for algebraic datatypes (ADT). A data type can be thought of as a disjoint union of tuples (or a "sum of products"). They are easy to define and easy...

additivity: for any sequence ( A j ) {\displaystyle (A_{j})} of pairwise disjoint subsets of R {\displaystyle \mathbb {R} } φ ( ⋃ i = 1 ∞ A i ) = ∑ i = 1...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

A 1 , A 2 , … ∈ R {\displaystyle A_{1},A_{2},\ldots \in R} of pairwise disjoint sets whose union lies in R , {\displaystyle R,} μ 0 ( ⋃ n = 1 ∞ A n ) =...

gravitational description. Consider a bipartite system consisting of two disjoint boundary regions A {\displaystyle A} and B {\displaystyle B} in a CFT....

a different meaning, of a decomposition of a topological space X into disjoint subsets each of which is a topological manifold (so that in particular...

{\displaystyle y} such that x {\displaystyle x} and y {\displaystyle y} are disjoint sets. ( L , ∈ ) {\displaystyle (L,\in )} is a substructure of ( V , ∈ )...

conjecture: for matroids of rank n {\displaystyle n} with n {\displaystyle n} disjoint bases B i {\displaystyle B_{i}} , it is possible to create an n × n {\displaystyle...

spaces is again a Hausdorff space; this comes from a simple preservation of disjoint open neighborhoods under the inverse of canonical projections from X i...

Conference. The University of Alabama at Birmingham. March 14–16, 2019. Almost disjoint families, set theory 2017 Balázs Strenner Hale Visiting assistant professor...

same construct (coincident sets); or that they were distinct constructs (disjoint sets). A number of researchers include creativity, either explicitly or...

programming language which is largely programmed and proven correct in Rocq. Disjoint-set data structure: correctness proof in Rocq was published in 2007. Feit–Thompson...

identification. The case of the construction of vector bundles from data on a disjoint union of topological spaces is a straightforward place to start. Suppose...

said to be pseudonormal if given two disjoint closed sets in it, one of which is countable, there are disjoint open sets containing them. Note the following:...

rhythms sounded less portentous but also less meaningful. He added that "the disjoint opacity of the lyrics fails to conceal Byrne's confusion about what it...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

connected subgraphs of G that all touch each other: for every pair of disjoint subgraphs, there must exist an edge in G that has one endpoint in each...

Hausdorff (T2), regular or normal because no two nonempty open sets are disjoint (that is, it is hyperconnected). The double-pointed cofinite topology is...

In an affine plane, two lines are called parallel if they are equal or disjoint. Using this definition, Playfair's axiom above can be replaced by: Given...

pronunciation, but sometimes in transcriptions (with the diacritics omitted). This disjoint between transcription and spoken value explains the romanisation for Sanskrit...

viscounties, lands, lordships in this our kingdom, be and remained disunited, disjoint and separate of our house of France not to be in any way included or merged...

range of verses (John 3:16–17); book chapter:verse1,verse2 for multiple disjoint verses (John 6:14, 44). The range delimiter is an en-dash, and there are...

AcN = {BncN} contained in F such that each collection Ai consists of disjoint balls, and E ⊆ ⋃ i = 1 c N ⋃ B ∈ A i B . {\displaystyle E\subseteq \bigcup...

dimension if every open cover of the space has a refinement that is a cover by disjoint open sets. A topological space is zero-dimensional with respect to the...

countable subfamily F ′ {\displaystyle {\mathcal {F}}'} consisting of disjoint balls such that ⋃ B ∈ F B ⊂ ⋃ B ∈ F ′ 5 B {\displaystyle \bigcup _{B\in...

reversal facilities and single line movement took place in that section. Both disjoint sections were finally bridged on 6 August 2021. In December 2024, trial...

their triples partitioned into (n-1)/2 sets each having (n/3) pairwise disjoint triples. This is called resolvable and such systems are called Kirkman...

can the complete graph K n {\displaystyle K_{n}} be decomposed into edge-disjoint copies of G {\displaystyle G} ? More unsolved problems in mathematics In...

to the one-point compactification of the union of a countable family of disjoint open intervals. The Hawaiian earring is a one-dimensional, compact, locally...

optimal time bound O ( n + k ) {\displaystyle O(n+k)} . The Maximum sum k-disjoint subarrays can also be computed in the optimal time bound O ( n + k ) {\displaystyle...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

{\displaystyle X_{1}} and X 2 {\displaystyle X_{2}} are open, connected, disjoint sets in R 2 {\displaystyle \mathbb {R} ^{2}} such that ∂ X 1 = ∂ X 2 {\displaystyle...

For efficiency, LSM trees often divide disk components into smaller, disjoint key ranges. In this way, when processing a range query, the system can...

utilized in definitions; for example, Cantor defined two sets as being disjoint if their intersection has an absence of points; however, it is debatable...

The parameter space Θ {\displaystyle \Theta } is partitioned into two disjoint sets Θ 0 {\displaystyle \Theta _{0}} and Θ 1 {\displaystyle \Theta _{1}}...

{\displaystyle y_{0}} ) the wedge sum of X and Y is the quotient space of the disjoint union of X and Y by the identification x 0 ∼ y 0 : {\displaystyle x_{0}\sim...

The R27 is a provincial route in South Africa that consists of two disjoint segments. The first segment, also known as the West Coast Highway, connects...

Free regular set, a subset of a topological space that is acted upon disjointly under a given group action Regular homotopy Regular isotopy in knot theory...

Hausdorff) spaces, i.e., all topological spaces in which distinct points have disjoint neighbourhoods. In another direction, every sober space (which may not...

surfaces occur in computer-aided design, where a surface is broken apart into disjoint pieces, with the derivatives of local parametrizations failing to even...

connected by k {\displaystyle k} vertex-disjoint paths. Since these paths must leave the two vertices of the pair via disjoint edges, a k {\displaystyle k} -vertex-connected...

{\displaystyle S} can be decomposed into the union of κ {\displaystyle \kappa } disjoint stationary sets; With Stanley Tennenbaum, developing the method of iterated...

Conversely, if two squares intersect in a vertex, then their two diagonals disjoint from this vertex form two opposite sides of a (possibly non-convex) midsquare...

and T {\displaystyle T} are separated precisely when they are disjoint and each is disjoint from the other's derived set S ′ ∩ T = ∅ = T ′ ∩ S . {\textstyle...

Continuum hypothesis Countable set Decidable set Denumerable set Disjoint sets Disjoint union Domain of a function Effective enumeration Element (mathematics)...

spaces (a topological space is c.c.c. if it has no uncountable, pairwise disjoint collection of open sets). Various other axioms modeled after Martin's axiom...

that enable a single-pass compiler to check that parallel processes are disjoint, even if the processes use procedures with global variables, eliminating...

composition Pc = Pc(X, Y) of two TTGs X and Y is a TTG created from the disjoint union of graphs X and Y by merging the sources of X and Y to create the...

biconnected for k ≥ 2 and triconnected for k ≥ 3. Every graph decomposes into a disjoint union of 1-connected components. 1-connected graphs decompose into a tree...

Kawarabayashi, Ken-ichi; Kobayashi, Yusuke; Reed, Bruce (2012). "The disjoint paths problem in quadratic time". Journal of Combinatorial Theory. Series...

generality that the sets B {\displaystyle B} and β {\displaystyle \beta } are disjoint. By the initial assumption, | B ∪ β | = | ( B ∪ β ) × ( B ∪ β ) | , {\displaystyle...

in undirected graphs, intersection of sets (or, more precisely, non-disjointness) is a symmetric relation. This gives rise to the study of intersection...

Hallfreðar saga the poet Hallfreðr composed a drápa on the jarl. Several disjoint stanzas by Hallfreðr in Skáldskaparmál are often thought to belong to this...

K-ary tree And–or tree (a,b)-tree Link/cut tree SPQR-tree Spaghetti stack Disjoint-set data structure (Union-find data structure) Fusion tree Enfilade Exponential...

For instance, a polygon with h holes bounded by simple integer polygons, disjoint from each other and from the boundary, has area A = i + b 2 + h − 1. {\displaystyle...

Stable marriage problem - a one-to-one matching between agents of two disjoint groups, each of whom has strict preferences over agents of the other group...

\varinjlim A_{i}} and is defined as follows. Its underlying set is the disjoint union of the A i {\displaystyle A_{i}} 's modulo a certain equivalence...

parkour began to grow in popularity during the mid-2000s, and today, several disjoint organizations produce competitions under the title of Parkour World Championships...

regular octahedron, but with dihedral angles that are non-convex along three disjoint edges. Because it has no interior diagonals, it cannot be triangulated...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

edges, and the subgraph of red and green edges each form a collection of disjoint cycles that together cover all edges of the graph twice. Therefore, every...

of discourse of any structure of that signature is then fragmented into disjoint subsets, one for every sort. When reasoning about biological organisms...

[ L : U ] = [ K ∪ L : U ] {\displaystyle [K:U]+[L:U]=[K\cup L:U]} for disjoint compact sets K , L ⊆ G {\displaystyle K,L\subseteq G} provided that U {\displaystyle...

structures; moreover, it forms a variation of Hodge structure, and X is a finite disjoint union of hermitian symmetric domains. Let Aƒ be the ring of finite adeles...

to Integer&Integer | String&Integer, which, as String and Integer are disjoint types, is equivalent to Integer&Integer | Nothing (Nothing is the empty...

structure (P, L, I) consists of a set P whose elements are called points, a disjoint set L whose elements are called lines and an incidence relation I between...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

U {\displaystyle U} in C {\displaystyle C} is disjoint from V U {\displaystyle V_{U}} and hence disjoint from W {\displaystyle W} , which contains x {\displaystyle...

problem, one is given a family of sets, and must choose a subfamily of disjoint sets that has the same union. One way of formulating a Sudoku puzzle in...

r | = 1 {\displaystyle |ps-qr|=1} and otherwise these two circles are disjoint. Ford circles are a special case of mutually tangent circles; the base...

that the edges spanning the cut between these two subsets form two vertex-disjoint complete bipartite graphs. When a graph has a 2-join, it may be decomposed...

An independent set in a geometric intersection graph is just a set of disjoint (non-overlapping) shapes. The problem of finding maximum independent sets...

F/\mathbb {F} _{q}} of degree one, and G {\displaystyle G} be a divisor with disjoint support from D {\displaystyle D} . The algebraic geometry code C L ( D...

product types and sum types are analogous to the cartesian product and disjoint union of abstract algebraic structures, quotient types reflect the concept...

_{i}(V)\subseteq V,} where the sets in union on the left are pairwise disjoint. The open set condition is a separation condition that ensures the images...

B)={{|A\cap B|} \over {|A\cup B|}}.} This value is 0 when the two sets are disjoint, 1 when they are equal, and strictly between 0 and 1 otherwise. Two sets...

evident in a statistical population Cluster graph, in graph theory, a disjoint union of complete graphs Clusterable graph, in balance theory Cluster algebra...

operad where P ( n ) {\displaystyle P(n)} consists of ordered lists of n disjoint disks inside the unit disk of R 2 {\displaystyle \mathbb {R} ^{2}} centered...

bumblebee (Bombus sichelii) is a species of bumblebee. Bombus sichelii is disjointly distributed in several subspecies in Eurasia: in the Cantabrian Mountains...

.. < θK−1. This set of thresholds divides the real number line into K disjoint segments, corresponding to the K response levels. The model can now be...

Krull shows that there exists an ideal of R maximal with respect to being disjoint from S, and moreover the ideal must be prime. This can be further generalized...

center, belongs to exactly one of the circles in the pencil. Every two disjoint circles, and every hyperbolic pencil of circles, may be transformed into...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

topological space is said to be connected if it is not the union of two disjoint nonempty open sets. A set is open if it contains no point lying on its...

{0,1}} depending on the number of dimensions. Fundamentally ESBT(Edge-disjoint Spanning Binomial Trees) is based on hypercube graphs, pipelining( m {\displaystyle...

can be expressed as the difference of two positive measures supported on disjoint sets. This can be extended to the noncommutative setting. Theorem—Every...

remarked by Jacques Roubaud that these two novels draw words from two disjoint sets of the French language, and that a third novel would be possible,...

(such as "first" and "last", "beginning" and "end", "entry" and "exit"). disjoint opposites (or "incompatibles"), members of a set which are mutually exclusive...

{\displaystyle G=BWB=\bigsqcup _{w\in W}BwB} of G {\displaystyle G} as a disjoint union of double cosets of B {\displaystyle B} parameterized by the elements...

In contrast, a parallel interrupted Mollweide projection uses multiple disjoint central meridians, giving the effect of multiple ellipses joined at the...

any open set is a disjoint union of sets in it. Compare this with base in topology, which is less restrictive as it allows non-disjoint unions. Theorem...

Alon–Yuster conjecture relating the chromatic numbers of graphs to the number of disjoint copies of a smaller graph that can be found in a larger one, later proven...

{K}}^{-n}(X_{+}).} Here X + {\displaystyle X_{+}} is X {\displaystyle X} with a disjoint basepoint labeled '+' adjoined. Finally, the Bott periodicity theorem as...

Jefferson County governments in 2003, the new Louisville Metro has several disjoint parcels of land throughout the county, of which some are enclaves in other...

belief that they would have the largest possible total area of any three disjoint circles within the triangle. Malfatti's problem has been used to refer...

(a(x),x]} , parametrized by x ∈ C {\displaystyle x\in C} , are pairwise disjoint, the function q : C → Q {\displaystyle q:C\to \mathbb {Q} } is injective...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Product A × B {\displaystyle A\times B} A ∧ B {\displaystyle A\wedge B} Disjoint union A + B {\displaystyle A+B} A ∨ B {\displaystyle A\vee B} Booleans...

Hill Road to State Highway 7 (MN 7), and a section that connected the two disjoint sections of County Road 5, passing between Cedar Lake and Lake Of The Isles...

space, then the following two properties are equivalent: If A and B are disjoint closed subsets whose union separates X, then either A or B separates X...

defined by the disjoint union of sets, and corresponds to a choice between structures. For species F and G, define (F + G)[A] to be the disjoint union (also...

U {\displaystyle U} indexed by an element of U {\displaystyle U} , All disjoint unions of all families of elements of U {\displaystyle U} indexed by an...

{\displaystyle y} such that x {\displaystyle x} and y {\displaystyle y} are disjoint sets. ∀ x [ ( ∃ a ( a ∈ x ) ) ⇒ ∃ y ( y ∈ x ∧ ¬ ∃ z ( z ∈ y ∧ z ∈ x ) )...

has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other. The logarithmic spiral or the pictured Archimedean...

- Krishna Park Extension extension, opened on 5 January 2026, and the disjoint Majlis Park - Deepali Chowk section opened on 8 March 2026. Currently,...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

generalizations of the hyperplane separation theorem, which states that two disjoint nonempty convex subsets of a finite-dimensional space R n {\displaystyle...

quasi-polynomial time, and can be solved in that time, including finding a large disjoint set of unit disks from a given set of disks in the hyperbolic plane, and...

mid cap segments (i.e. top 85% of total market cap), rather than as a disjoint segment. CRSP also defines a "core cap" segment, consisting of all segments...

{\displaystyle (v_{1}+v_{2},k,t)} -covering can be assembled from coverings on disjoint sets of sizes v 1 {\displaystyle v_{1}} and v 2 {\displaystyle v_{2}} ...

in the packing should be separable using only guillotine cuts. Maximum disjoint set (or Maximum independent set) is a problem in which both the sizes and...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

are linearly separable precisely when their respective convex hulls are disjoint (colloquially, do not overlap). Three non-collinear points in two classes...

Given a tour, delete k mutually disjoint edges. Reassemble the remaining fragments into a tour, leaving no disjoint subtours (that is, do not connect...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Radon's theorem to the set A = {x1, ..., xn}, which furnishes us with disjoint subsets A1, A2 of A such that the convex hull of A1 intersects the convex...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

Then λ is said to be in the residual spectrum of T, σr(T). So σ(T) is the disjoint union of these three sets, σ ( T ) = σ p ( T ) ∪ σ c ( T ) ∪ σ r ( T )...

{\textstyle \tau \in X} such that σ , τ {\textstyle \sigma ,\tau } are disjoint and τ ∪ σ {\textstyle \tau \cup \sigma } is a face of X: Lk ⁡ ( σ , X )...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

smallest closed ball centered at x {\displaystyle x} which intersects any two disjoint features (vertices or edges) of the graph. Definitions of local feature...

called biseparable, if one can find a partition of the parties in two disjoint subsets A {\displaystyle A} and B {\displaystyle B} with A ∪ B = { 1 ,...

not share any parts in common, opposite of overlap, emphasizing the disjointness of the objects. unrestricted fusion A principle in mereology allowing...

once. If we operate on M by all the elements of A or of B, we get two disjoint sets whose union is all points but the origin. Now we take some figure...

space is said to be ultraconnected if no two nonempty closed sets are disjoint. Equivalently, a space is ultraconnected if and only if the closures of...

note that in a true multiverse theory, "the universes are then completely disjoint and nothing that happens in any one of them is causally linked to what...

and her husband Spink continue to deal with events in Gettys. Nevare's disjoint personalities are united to realize the initial goal of the magic, in spite...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

set of terminal symbols with N {\displaystyle N} and T {\displaystyle T} disjoint, P {\displaystyle P} is a finite set of production rules of the form α...

1382–1393. From this paper: Definitions: A planar map is a set of pairwise disjoint subsets of the plane, called regions. A simple map is one whose regions...

desired depth of ranking. These approaches have the advantages of addressing disjoint sets, sets of different sizes, and top-weightedness (taking into account...

I}A_{i}} , rather than an injection, there is no requirement that the sets be disjoint. Proof: For (1) observe that if T {\displaystyle T} is countable there...

sets of the Turán graph as a disjoint union of isolated vertices. Then, the overall graph is the complement of the disjoint union of the complements of...

also has the same nonzero probability, and since any two rotations are disjoint, their union has infinite probability, which is a contradiction.[clarification...

to be "a string of constant symbols from Σ and variable symbols from a disjoint set". The language of such a pattern is the set of all its nonempty ground...

called a cycle of the permutation. Every permutation can be decomposed into disjoint cycles, that is, cycles which have no common elements. The permutation...

self-training in which multiple classifiers are trained on different (ideally disjoint) sets of features and generate labeled examples for one another. Human...

Operations Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union Concepts...

of this as a "Panorama", the recorded image is simply a collage of five disjoint images. [So many panoramas were taken during the EVAs that they are better...

the 20th century to the present time of the novel, these are: The Era of Disjoint World The Era of World Reunion   (people of the world uniting together...

extension axiom E A n , m {\displaystyle EA_{n,m}} says that for any two disjoint subsets X {\displaystyle X} and Y {\displaystyle Y} of respective cardinality...

left or right. A simulation of this algorithm working can be found here. Disjoint (where walls are not connected to the outer boundary/boundary is not closed)...

the disjoint union of two sets, then we can solve the problem by enumerating the first set and then the second set. If the union is non disjoint but the...

non-negative integer k, partition the set S = { 0, 1, ..., N − 1 } into two disjoint subsets S0 and S1 that have equal sums of powers up to k, that is: ∑ x...

Monotone function So for instance, these intervals need not be pairwise disjoint nor is it required that they intersect only at endpoints. It is even possible...