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{{short description|Area of combinatorics in mathematics}} ...classical [[Freiman's theorem]] provides a partial answer to this question in terms of [[multi-dimensional arithmetic progression]]s. ...

...= Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry | subject = [[Topological combinatorics]] ...

...en by Francine Blanchet-Sadri, and published in 2008 by Chapman & Hall/CRC in their Discrete Mathematics and its Applications book series. ...o repetition. Part four concerns codes defined from sets of partial words, in the sense that no two distinct concatenations of partial words from the set ...

...[[Ivan Rival]] and Bill Sands in 1981. It was proved by [[Lawrence Shepp]] in ...epp|1982}}. An extension was given by [[Peter C. Fishburn|Peter Fishburn]] in {{harvtxt|Fishburn|1984}}. ...

...e longest increasing subsequence in the limit. The theorem was influential in [[probability|probability theory]] since it connected the [[Kardar–Parisi–Z The theorem was proven in 1999 by [[Jinho Baik]], [[Percy Deift]] and [[Kurt Johansson (mathematician ...

...mechanics]] and [[Combinatorics#Probabilistic_combinatorics|probabilistic combinatorics]] (especially [[random graph]]s and the [[probabilistic method]]). for all ''x'', ''y'' in the lattice, then ...

{{short description|Theorem in arithmetic combinatorics on finite partitions of the natural numbers}} ...''' is a [[theorem]] in mathematics, and more particularly in [[arithmetic combinatorics]] and [[Ramsey theory]]. According to this theorem, whenever the [[natural ...

...tation of the symmetric group]] <math>S_n</math> to be zero. It was proven in 1988 by Carlos Gamas.<ref name="Gamas">{{cite journal ...presentation. The tensor <math>v_1 \otimes v_2 \otimes \dots \otimes v_n \in V^{\otimes n}</math> symmetrized by <math>\chi^{\lambda}</math> is defined ...

In [[combinatorics|combinatorial]] mathematics, '''Baranyai's theorem''' (proved by and named ...math> different ways, in such a way that each ''r''-element subset appears in exactly one of the partitions. ...

...]] combinatorics''' is a field in the intersection of [[number theory]], [[combinatorics]], [[ergodic theory]] and [[harmonic analysis]]. ...rations (addition, subtraction, multiplication, and division). [[Additive combinatorics]] is the special case when only the operations of addition and subtraction ...

{{short description|Asymptotic estimate in group theory}} In [[finite group|finite group theory]], the '''Higman–Sims asymptotic formula ...

...rican Mathematical Society| year=1965}}</ref> a simplified proof was given in 1976 by A. Pinkus.<ref name="Pinkus 1976">{{cite journal|last=Pinkus|first= Define a ''signed partition'' as a partition in which each subinterval <math>i</math> has an associated sign <math>\delta_i ...

[[File:TuckerLemExample.png|thumb|350px|In this example, where n=2, the red 1-simplex has vertices which are labelled In [[mathematics]], '''Tucker's lemma''' is a [[combinatorics|combinatorial]] analog of the [[Borsuk&ndash;Ulam theorem]], named after [[ ...

...Hilton''' (born 4 April 1941) is a British mathematician specializing in [[combinatorics]] and [[graph theory]]. His current positions are as [[emeritus]] professor ...~smshiltn/ Personal Homepage]</ref> His dissertation was "Representation Theorems for Integers and Real Numbers" under his advisor David E. Daykin.<ref name= ...

...ions. There is a special re-labelling operation that re-labels the objects in the slots, assigning labels from 1 to ''k'', where ''k'' is the total numbe In particular, if ''G'' is the [[symmetric group]] of order ''n'' (hence, |''G ...

...]], '''Mnëv's universality theorem''' is a result in the intersection of [[combinatorics]] and [[algebraic geometry]] used to represent [[algebraic manifold|algebra ...n also be understood as the statement that point configurations of a fixed combinatorics can show arbitrarily complicated behavior. ...

...ion|One of several related theorems regarding the sizes of certain sumsets in abelian groups}} ...lian group]]s. These are named after [[Martin Kneser]], who published them in 1953<ref name = Kneser53>{{cite journal | first=Martin | last=Kneser | titl ...

...wed that a certain finitistic theorem in [[Ramsey theory]] is not provable in Peano arithmetic (PA). ...on, denoted by <math>(*)</math> in the original reference, is not provable in PA: ...

{{short description|Result in enumerative combinatorics and linear algebra}} ...t was discovered by [[Percy Alexander MacMahon|Percy MacMahon]] and proved in his monograph ''Combinatory analysis'' (1916). It is often used to derive ...

{{dablink|For other theorems of Jacobi see [[Jacobi's theorem (disambiguation)]].}} In [[number theory]], '''Jacobi's four-square theorem''' gives a formula for t ...