This group gathers theorems about counting and arranging, the part of combinatorics concerned with how many objects of a given kind exist and how they are structured. It covers formulas for binomial and multinomial coefficients, counting under symmetry, block designs and Latin squares, ordered sets and their chains and antichains, additive combinatorics, and the combinatorics of coding theory. A theorem belongs here when its cited article places it in combinatorics but not in graph theory or Ramsey theory.
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Enumerative, Additive and Algebraic Combinatorics
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Abel's binomial theorem (Wikipedia)
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Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients.
Corners theorem (Wikipedia)
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In arithmetic combinatorics, the corners theorem states that
Lambek-Moser theorem (Wikipedia)
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The Lambek-Moser theorem is a mathematical description of the partitions of natural numbers into two complementary sets.
Multinomial theorem (Wikipedia)
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In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum.
Dilworth's Theorem (Wikipedia)
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In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite
Mirsky's theorem (Wikipedia)
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In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of
Baranyai's theorem (Wikipedia)
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In combinatorial mathematics, Baranyai's theorem (proved by and named after
Fisher's inequality (Wikipedia)
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of subsets that satisfy certain prescribed conditions in combinatorial mathematics. Outlined by Ronald Fisher, a population geneticist
Polya enumeration theorem (Wikipedia)
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Redfield-Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately generalizes
Sperner's lemma (Wikipedia)
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In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous
Burnside's Lemma (Wikipedia)
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Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy-Frobenius lemma, or the orbit-counting
Kruskal-Katona theorem (Wikipedia)
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In algebraic combinatorics, the Kruskal-Katona theorem gives a complete
Bertrand's Ballot Theorem (Wikipedia)
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In combinatorics, Bertrand's ballot problem is the question: "In
Elias Bassalygo bound (Wikipedia)
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The Elias Bassalygo bound is a mathematical limit used in coding theory for error correction during data transmission
Aztec diamond (Wikipedia)
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In combinatorial mathematics, an Aztec diamond of order n consists of all
Bondy's theorem (Wikipedia)
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family of sets from each other. It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published
Bruck-Ryser-Chowla theorem (Wikipedia)
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The Bruck-Ryser-Chowla theorem is a result on the combinatorics of symmetric block designs that implies nonexistence
Dinitz theorem (Wikipedia)
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In combinatorics, the Dinitz theorem, formerly known as the Dinitz
Freiman's theorem (Wikipedia)
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In additive combinatorics, a discipline within mathematics, Freiman's theorem
MacMahon's master theorem (Wikipedia)
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MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy
Bregman-Minc inequality (Wikipedia)
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In discrete mathematics, the Bregman-Minc inequality, or Bregman's theorem
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