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96 relations: Abstract algebra, Algebra, Algorithm, Alphabet, American Mathematical Society, Andrey Markov Jr., Arithmetic progression, Astronomy, Axel Thue, Émile Baudot, Bartel Leendert van der Waerden, Binary number, Binary relation, Calculus, Cambridge University Press, Carl Friedrich Gauss, Character encoding, Combinatorics, Commutator, Computer programming, Computer science, Conjugacy class, Context-free language, Context-sensitive language, Curve, Cycle (graph theory), De Bruijn, Decision problem, Discrete mathematics, Distinct (mathematics), Dominique Perrin, Emil Leon Post, Empty set, English alphabet, Equation, Factorization, Fibonacci word, Finite set, Finite-state machine, Formal language, Frank P. Ramsey, Free group, Generator (mathematics), Graph (discrete mathematics), Group theory, Hierarchy, Infinite set, Inverse element, Joseph-Louis Lagrange, Kolakoski sequence, ..., Levi's lemma, Lyndon word, M. Lothaire, Marston Morse, Mathematical analysis, Mathematics, Modular arithmetic, Monoid factorisation, Morse code, Music, Necklace (combinatorics), Nielsen transformation, Noam Chomsky, Parity (mathematics), Partial word, Permutation group, Plane (geometry), Post correspondence problem, Product (mathematics), Recursively enumerable language, Regular language, Schützenberger, Semigroup, Sequence, Sesquipower, Set (mathematics), Shift space, Square-free word, String operations, Sturmian word, Subset, Symbol, Thue–Morse sequence, Tree structure, Unavoidable pattern, Undecidable problem, Uniqueness quantification, Vertex (graph theory), Walther von Dyck, William Burnside, Wojciech Rytter, Word (group theory), Word metric, Word problem (mathematics), Word problem for groups, Young–Fibonacci lattice. Expand index (46 more) »
Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Alphabet
An alphabet is a standard set of letters (basic written symbols or graphemes) that is used to write one or more languages based upon the general principle that the letters represent phonemes (basic significant sounds) of the spoken language.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Andrey Markov Jr.
Andrey Andreyevich Markov Jr. (Андре́й Андре́евич Ма́рков; St. Petersburg, September 22, 1903 – Moscow, October 11, 1979) was a Soviet mathematician, the son of the Russian mathematician Andrey Andreyevich Markov Sr, and one of the key founders of the Russian school of constructive mathematics and logic.
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Arithmetic progression
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
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Astronomy
Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.
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Axel Thue
Axel Thue (19 February 1863 – 7 March 1922), was a Norwegian mathematician, known for highly original work in diophantine approximation, and combinatorics.
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Émile Baudot
Jean-Maurice-Émile Baudot (11 September 1845 – 28 March 1903), French telegraph engineer and inventor of the first means of digital communication Baudot code, was one of the pioneers of telecommunications.
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Bartel Leendert van der Waerden
Bartel Leendert van der Waerden (February 2, 1903 – January 12, 1996) was a Dutch mathematician and historian of mathematics.
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Binary number
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
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Character encoding
Character encoding is used to represent a repertoire of characters by some kind of encoding system.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
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Computer programming
Computer programming is the process of building and designing an executable computer program for accomplishing a specific computing task.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Context-free language
In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG).
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Context-sensitive language
In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar).
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
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Cycle (graph theory)
In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself.
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De Bruijn
De Bruijn is a Dutch surname meaning "the brown".
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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Distinct (mathematics)
In mathematics, two things are called distinct if they are not equal.
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Dominique Perrin
Dominique Pierre Perrin (b. 1946) is a French mathematician and theoretical computer scientist known for his contributions to coding theory and to combinatorics on words.
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Emil Leon Post
Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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English alphabet
The modern English alphabet is a Latin alphabet consisting of 26 letters, each having an uppercase and a lowercase form: The same letters constitute the ISO basic Latin alphabet.
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Equation
In mathematics, an equation is a statement of an equality containing one or more variables.
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Factorization
In mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
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Fibonacci word
A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet).
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Finite-state machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.
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Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
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Frank P. Ramsey
Frank Plumpton Ramsey (22 February 1903 – 19 January 1930) was a British philosopher, mathematician and economist who made fundamental contributions to abstract algebra before his death at the age of 26.
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Free group
In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st.
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Generator (mathematics)
In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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Hierarchy
A hierarchy (from the Greek hierarchia, "rule of a high priest", from hierarkhes, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another A hierarchy can link entities either directly or indirectly, and either vertically or diagonally.
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Infinite set
In set theory, an infinite set is a set that is not a finite set.
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Inverse element
In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.
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Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
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Kolakoski sequence
In mathematics, the Kolakoski sequence, sometimes also known as the Oldenburger-Kolakoski sequence, is an infinite sequence of symbols that is its own run-length encoding and the prototype for an infinite family of related sequences.
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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.
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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.
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M. Lothaire
M.
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Marston Morse
Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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Monoid factorisation
In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets.
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Morse code
Morse code is a method of transmitting text information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment.
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Music
Music is an art form and cultural activity whose medium is sound organized in time.
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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.
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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 a non-commutative analogue of row reduction and one of the main tools used in studying free groups,.
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Noam Chomsky
Avram Noam Chomsky (born December 7, 1928) is an American linguist, philosopher, cognitive scientist, historian, social critic and political activist.
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Parity (mathematics)
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
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Partial word
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 symbol value is not known or not specified.
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Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Post correspondence problem
The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946.
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Product (mathematics)
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.
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Recursively enumerable language
In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language.
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Regular language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be expressed using a regular expression, in the strict sense of the latter notion used in theoretical computer science (as opposed to many regular expressions engines provided by modern programming languages, which are augmented with features that allow recognition of languages that cannot be expressed by a classic regular expression).
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Schützenberger
Schützenberger may refer to these people.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Sesquipower
In mathematics, a sesquipower or Zimin word is a string over an alphabet with identical prefix and suffix.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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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.
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Square-free word
In combinatorics, a square-free word is a word (a sequence of characters) that does not contain any subword twice in a row.
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String operations
In computer science, in the area of formal language theory, frequent use is made of a variety of string functions; however, the notation used is different from that used for computer programming, and some commonly used functions in the theoretical realm are rarely used when programming.
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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.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Symbol
A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship.
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Thue–Morse sequence
In mathematics, the Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far.
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Tree structure
A tree structure or tree diagram is a way of representing the hierarchical nature of a structure in a graphical form.
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Unavoidable pattern
In mathematics and theoretical computer science, an unavoidable pattern is a pattern of symbols that must occur in any sufficiently long string over an alphabet.
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Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.
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Uniqueness quantification
In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists.
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Vertex (graph theory)
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
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Walther von Dyck
Walther Franz Anton von Dyck (6 December 1856 in Munich – 5 November 1934 in Munich), born Dyck and later ennobled, was a German mathematician.
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William Burnside
(William Snow Burnside was an Irish mathematician, often confused with the English mathematician.) William Burnside (2 July 1852 – 21 August 1927) was an English mathematician.
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Wojciech Rytter
Wojciech Rytter is a Polish computer scientist, a professor of computer science at the University of Warsaw.
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Word (group theory)
In group theory, a word is any written product of group elements and their inverses.
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Word metric
In group theory, a branch of mathematics, a word metric on a group G is a way to measure distance between any two elements of G. As the name suggests, the word metric is a metric on G, assigning to any two elements g, h of G a distance d(g,h) that measures how efficiently their difference g^ h can be expressed as a word whose letters come from a generating set for the group.
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Word problem (mathematics)
In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set.
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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 words in the generators represent the same element.
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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.
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References
[1] https://en.wikipedia.org/wiki/Combinatorics_on_words
