Combinatorics on words

set of strings of symbols that may be constrained by rules that are specific to it; words whose letters are taken from an alphabet and are well-formed according to a specific set of rules

data type representing a finite sequence of encoded characters

non-empty set of symbols or letters that make up strings in a formal language

specification of a mathematical group by generators and relaions

thumb|The distribution of permutations in a 3-symbol superpermutation In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation concatenated together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed. For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations.

a sequence of integers formed by rounding down the integer multiples of a positive irrational number

a “generic” algebraic structure over the given set, fulfilling no other equations except those given by the defining axioms

Mathematical concept

theorem about sufficient conditions for ensuring that that several elements in a group acting on a set freely generate a free subgroup of that group

an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent

concept in mathematics

Mathematical concept named for Ernst Witt

basic construction of combinatorial group theory

String that is strictly smaller in lexicographic order than all of its rotations

graph invariant

subfield in mathematics

written product of elements of a mathematical group and their inverses

way to measure distance between any two elements of group (in group theory)

given a finitely generated group, the algorithmic problem of deciding whether two words in the generators represent the same element

in mathematics, some kind of formal language

a sequence of symbols that does not contain any repeated contiguous subsequence