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Stanley–Wilf conjecture

The Stanley–Wilf conjecture, formulated independently by Richard P. Stanley and Herbert Wilf in the late 1980s, states that the growth rate of every proper permutation class is singly exponential. It

Chomsky–Schützenberger representation theorem

In formal language theory, the Chomsky–Schützenberger representation theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about representing a given context-free language in ter

Erdős–Ko–Rado theorem

In mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. Paul Erdős, Chao Ko, and Richard Rado proved the t

Noisy-channel coding theorem

In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is

Analyst's traveling salesman theorem

The analyst's traveling salesman problem is an analog of the traveling salesman problem in combinatorial optimization. In its simplest and original form, it asks which plane sets are subsets of rectif

Erdős–Anning theorem

The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdős and Norman

Myhill–Nerode theorem

In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who prove

Buchholz hydra

In mathematical logic, the Buchholz hydra game is a hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree. The hydra game can be used to generate a rap

Schur's theorem

In discrete mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur. In functional analysis, Schu

Dinitz conjecture

In combinatorics, the Dinitz theorem (formerly known as Dinitz conjecture) is a statement about the extension of arrays to partial Latin squares, proposed in 1979 by Jeff Dinitz, and proved in 1994 by

Erdős–Szekeres theorem

In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of le

Holland's schema theorem

Holland's schema theorem, also called the fundamental theorem of genetic algorithms, is an inequality that results from coarse-graining an equation for evolutionary dynamics. The Schema Theorem says t

Minimax

Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst

Rado's theorem (Ramsey theory)

Rado's theorem is a theorem from the branch of mathematics known as Ramsey theory. It is named for the German mathematician Richard Rado. It was proved in his thesis, Studien zur Kombinatorik.

Gibbard's theorem

In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decisi

Kemnitz's conjecture

In additive number theory, Kemnitz's conjecture states that every set of lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autum

Curtis–Hedlund–Lyndon theorem

The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon;

Arrow's impossibility theorem

Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternati

Erdős–Szemerédi theorem

The Erdős–Szemerédi theorem in arithmetic combinatorics states that for every finite set of integers, at least one of , the set of pairwise sums or , the set of pairwise products form a significantly

Theorem on friends and strangers

The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory.

Milliken's tree theorem

In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure than sets. Let T be a finitely splitting ro

Milliken–Taylor theorem

In mathematics, the Milliken–Taylor theorem in combinatorics is a generalization of both Ramsey's theorem and Hindman's theorem. It is named after Keith Milliken and Alan D. Taylor. Let denote the set

Large set (Ramsey theory)

In Ramsey theory, a set S of natural numbers is considered to be a large set if and only if Van der Waerden's theorem can be generalized to assert the existence of arithmetic progressions with common

Sprague–Grundy theorem

In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of

Akra–Bazzi method

In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorith

Tutte–Berge formula

In the mathematical discipline of graph theory the Tutte–Berge formula is a characterization of the size of a maximum matching in a graph. It is a generalization of Tutte theorem on perfect matchings,

Folkman's theorem

Folkman's theorem is a theorem in mathematics, and more particularly in arithmetic combinatorics and Ramsey theory. According to this theorem, whenever the natural numbers are partitioned into finitel

Friedman's SSCG function

In mathematics, a simple subcubic graph (SSCG) is a finite simple graph in which each vertex has degree at most three. Suppose we have a sequence of simple subcubic graphs G1, G2, ... such that each g

Star height problem

The star height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions of limited star height, i.e. with a limited nesting depth of

Pigeonhole principle

In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. For example, if one has three gloves

Cameron–Erdős conjecture

In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in is The sum of two odd numbers is even, so a set of odd numbers is always s

May's theorem

In social choice theory, May's theorem states that simple majority voting is the only anonymous, neutral, and positively responsive social choice function between two alternatives. Further, this proce

Hales–Jewett theorem

In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory named after Alfred W. Hales and Robert I. Jewett, concerning the degree to which high-dimensional object

Star of David theorem

The Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients. It was discovered by Henry W. Gould in 1972.

Chomsky–Schützenberger enumeration theorem

In formal language theory, the Chomsky–Schützenberger enumeration theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about the number of words of a given length generated by a

Parthasarathy's theorem

In mathematics – and in particular the study of games on the unit square – Parthasarathy's theorem is a generalization of Von Neumann's minimax theorem. It states that a particular class of games has

Schwenk's theorem

No description available.

Gibbard–Satterthwaite theorem

In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministi

Van der Waerden's theorem

Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden's theorem states that for any given positive integers r and k, there is some number N such tha

Kruskal's tree theorem

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding.

Bregman–Minc inequality

In discrete mathematics, the Bregman–Minc inequality, or Bregman's theorem, allows one to estimate the permanent of a binary matrix via its row or column sums. The inequality was conjectured in 1963 b

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