# Category: Combinatorics on words

Locally catenative sequence
In mathematics, a locally catenative sequence is a sequence of words in which each word can be constructed as the concatenation of previous words in the sequence. Formally, an infinite sequence of wor
Word problem for groups
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two wor
Word problem for semigroups
No description available.
String (computer science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length ch
Splicing rule
In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language genera
Free half group
No description available.
Grammar systems theory
Grammar systems theory is a field of theoretical computer science that studies systems of finite collections of formal grammars generating a formal language. Each grammar works on a string, a so-calle
Algorithmic Combinatorics on Partial Words
Algorithmic Combinatorics on Partial Words is a book in the area of combinatorics on words, and more specifically on partial words. It was written by Francine Blanchet-Sadri, and published in 2008 by
Hall word
In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on th
Free object
In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: th
Lyndon word
In mathematics, in the areas of combinatorics and computer science, a Lyndon word is a nonempty string that is strictly smaller in lexicographic order than all of its rotations. Lyndon words are named
Symbolic dynamics
In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which correspon
Unavoidable pattern
In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet.
Young–Fibonacci lattice
In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. An
Local language (formal language)
In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word
Automatic sequence
In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is
K-regular sequence
In mathematics and theoretical computer science, a k-regular sequence is a sequence satisfying linear recurrence equations that reflect the base-k representations of the integers. The class of k-regul
Autocorrelation (words)
In combinatorics, a branch of mathematics, the autocorrelation of a word is the set of periods of this word. More precisely, it is a sequence of values which indicate how much the end of a word looks
Automatic group
In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given
Cobham's theorem
Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condit
Dehn function
In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in th
Plactic monoid
In mathematics, the plactic monoid is the monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified with semistandard Young tableaux. It was dis
Recurrent word
In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquip
Hyperbolic group
In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metr
Word problem (mathematics)
In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word p
Formal language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alp
Levi's lemma
In theoretical computer science and mathematics, especially in the area of combinatorics on words, the Levi lemma states that, for all strings u, v, x and y, if uv = xy, then there exists a string w s
Nielsen transformation
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, Nielsen transformations, named after Jakob Nielsen, are certain automorphisms of a free group which are
Davenport–Schinzel sequence
In combinatorics, a Davenport–Schinzel sequence is a sequence of symbols in which the number of times any two symbols may appear in alternation is limited. The maximum possible length of a Davenport–S
Davenport–Schinzel Sequences and Their Geometric Applications
Davenport–Schinzel Sequences and Their Geometric Applications is a book in discrete geometry. It was written by Micha Sharir and Pankaj K. Agarwal, and published by Cambridge University Press in 1995,
Lattice word
In mathematics, a lattice word (or lattice permutation) is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1. A reverse latt
Involutive monoid
No description available.
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 per
Word (group theory)
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z−1xzz and y−1zxx−1yz−1 are words in the set {x, y,
Graham–Rothschild theorem
In mathematics, the Graham–Rothschild theorem is a theorem that applies Ramsey theory to combinatorics on words and combinatorial cubes. It is named after Ronald Graham and Bruce Lee Rothschild, who p
Necklace (combinatorics)
In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent. It represents a structure with n circularl
Compact semigroup
In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here does not refer to any topology on t
Necklace problem
The necklace problem is a problem in recreational mathematics concerning the reconstruction of necklaces (cyclic arrangements of binary values) from partial information.
Cyclically reduced word
In mathematics, cyclically reduced word is a concept of combinatorial group theory. Let F(X) be a free group. Then a word w in F(X) is said to be cyclically reduced if and only if every cyclic permuta
Small cancellation theory
In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have "smal
Combinatorics on words
Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the se
Train track map
In the mathematical subject of geometric group theory, a train track map is a continuous map f from a finite connected graph to itself which is a homotopy equivalence and which has particularly nice c
Free lattice
In mathematics, in the area of order theory, a free lattice is the free object corresponding to a lattice. As free objects, they have the universal property.
Alphabet (formal languages)
In formal language theory, an alphabet is a non-empty set of symbols/glyphs, typically thought of as representing letters, characters, or digits but among other possibilities the "symbols" could also
Beatty sequence
In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are
Free monoid
In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid ope
Random group
In mathematics, random groups are certain groups obtained by a probabilistic construction. They were introduced by Misha Gromov to answer questions such as "What does a typical group look like?" It so
Thue number
In the mathematical area of graph theory, the Thue number of a graph is a variation of the chromatic index, defined by and named after mathematician Axel Thue, who studied the squarefree words used to
Witt vector
In mathematics, a Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such a way that the ring of Witt v
Subshift of finite type
In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all poss
Van Kampen diagram
In the mathematical area of geometric group theory, a Van Kampen diagram (sometimes also called a Lyndon–Van Kampen diagram ) is a planar diagram used to represent the fact that a particular word in t
Partial word
In computer science and the study of combinatorics on words, a partial word is a string that may contain a number of "do not know" or "do not care" symbols i.e. placeholders in the string where the sy
Morphic word
In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. Every automat
Hobby–Rice theorem
In mathematics, and in particular the necklace splitting problem, the Hobby–Rice theorem is a result that is useful in establishing the existence of certain solutions. It was proved in 1965 by Charles
Critical exponent of a word
In mathematics and computer science, the critical exponent of a finite or infinite sequence of symbols over a finite alphabet describes the largest number of times a contiguous subsequence can be repe
Dejean's theorem
Dejean's theorem (formerly Dejean's conjecture) is a statement about repetitions in infinite strings of symbols. It belongs to the field of combinatorics on words; it was conjectured in 1972 by Franço
Parameter word
In the mathematical study of combinatorics on words, a parameter word is a string over a given alphabet having some number of wildcard characters. The set of strings matching a given parameter word is
Presentation of a group
In mathematics, a presentation is one method of specifying a group. A presentation of a group G comprises a set S of generators—so that every element of the group can be written as a product of powers
Necklace polynomial
In combinatorial mathematics, the necklace polynomial, or Moreau's necklace-counting function, introduced by C. Moreau, counts the number of distinct necklaces of n colored beads chosen out of α avail
Sturmian word
In mathematics, a Sturmian word (Sturmian sequence or billiard sequence), named after Jacques Charles François Sturm, is a certain kind of infinitely long sequence of characters. Such a sequence can b
Specht's theorem
In mathematics, Specht's theorem gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after Wilhelm Specht, who proved the theorem in 1940. Two m
Shift space
In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system. In fact, shift spaces and symbolic dyn
Necklace splitting problem
Necklace splitting is a picturesque name given to several related problems in combinatorics and measure theory. Its name and solutions are due to mathematicians Noga Alon and Douglas B. West. The basi
Sesquipower
In mathematics, a sesquipower or Zimin word is a string over an alphabet with identical prefix and suffix. Sesquipowers are unavoidable patterns, in the sense that all sufficiently long strings contai
Knuth–Bendix completion algorithm
The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system.
Word metric
In group theory, a word metric on a discrete group is a way to measure distance between any two elements of . As the name suggests, the word metric is a metric on , assigning to any two elements , of
HNN extension
In mathematics, the HNN extension is an important construction of combinatorial group theory. Introduced in a 1949 paper Embedding Theorems for Groups by Graham Higman, Bernhard Neumann, and Hanna Neu
Alternation (formal language theory)
In formal language theory and pattern matching, alternation is the union of two sets of strings, or equivalently the logical disjunction of two patterns describing sets of strings. Regular languages a
Ping-pong lemma
In mathematics, the ping-pong lemma, or table-tennis lemma, is any of several mathematical statements that ensure that several elements in a group acting on a set freely generates a free subgroup of t