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formal languages, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered. In the shortlex ordering, sequences...

sequence. This variant of the lexicographical order is sometimes called shortlex order. In lexicographical order, the word "Thomas" appears before "Thompson"...

D 6 ∗ / ∼ {\displaystyle {\mathcal {D}}_{6}^{*}/\sim } equipped with a shortlex order, where the equivalence class ∼ {\displaystyle \sim } is { n ∈ D 6...

some recursive order. For instance, the binary Champernowne sequence in shortlex order is 0 1 00 01 10 11 000 001 ... (sequence A076478 in the OEIS) where...

minimal element. See Shortlex for an alternative string ordering that preserves well-foundedness. For the example alphabet, the shortlex order is ε < 0 <...

0^{64}\ldots } obtained by splicing exponentially long strings of 0s into the shortlex ordering of all binary strings. Most of this sequence consists of long...

setting the nth bit of the sequence to 1 if and only if the nth string (in shortlex order) is in the language. This representation is useful in the diagonalization...

extra-large type are biautomatic (David Peifer). Artin groups of large type are shortlex automatic with regular geodesics (Derek Holt and Sarah Rees). Many other...

{\displaystyle <} among the words generated by X {\displaystyle X} (e.g., shortlex order). For each relation P i = Q i {\displaystyle P_{i}=Q_{i}} in R {\displaystyle...

numerals, in natural order of the integers represented, is automatically in shortlex order (shortest first, lexicographical within each length). Thus, using...

government, dynastic house, sovereign or organization to an individual Shortlex order, a method for ordering sequences in mathematics and formal language...

the rows, ordered by the shortlex order, and the elements of S {\displaystyle S} function as the columns, ordered by the shortlex order. Next, the cells...

S2CID 164277147 Holt, Derek F; Rees, Sarah (2012), "Artin groups of large type are shortlex automatic with regular geodesics", Proceedings of the London Mathematical...