Combinatorics

founded the field of discrete mathematics

The union-closed sets conjecture, also known as Frankl's conjecture, is an open problem in combinatorics posed by Péter Frankl in 1979.

generalises the concept of "path" from graphs to matroids

In combinatorial mathematics, Dobiński's formula states that the

In discrete mathematics, the Bregman-Minc inequality, or Bregman's theorem, allows one to estimate the permanent of a binary matrix

Ernst Straus was a German-born American mathematician who worked in a variety of areas including relativity and combinatorics.

renewed interest has been aroused in the notion of covering and related problems

Hajek conjecture, is a mathematical hypothesis in combinatorics concerning the maximum achieved by a particular function ϕ of matr

In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate

In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, o

od is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescr

In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that repr

In the mathematical field of combinatorics, the q-Pochhammer symbol, also called the q-shifted factorial, is the product ( a ; q )

In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number o

In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by

In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of thr

In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B re

In arithmetic combinatorics, Behrend's theorem states that the subsets of the integers from 1 to n in which no member of the set i

In combinatorics, the Dinitz theorem, formerly known as the Dinitz conjecture, is a statement about the extension of arrays to par

extremal combinatorics

combinatorics

combinatorics

combinatorics

combinatorics

Sperner's theorem

best known for his work in combinatorics

Various Problems in Extremal Combinatorics

especially noted in connection with the partitions of numbers and enumerative combinatorics

Choice and Chance: An Elementary Treatise on Permutations, Combinations, and Probability

best known for his work on Catalan numbers and alternating permutations

So fruitful, in fact, was Ramsey's theorem that today there is an entire branch of mathematics, known as Ramsey theory, which is dedicated to studying similar results.

Zsolt Baranyai (June 23, 1948 in Budapest, April 6, 1978) was a Hungarian mathematician known for his work in combinatorics.

Ben Joseph Green FRS (born 27 February 1977) is a British mathematician specialising in combinatorics and number theory.

Vera Turán Sós (11 September 1930-22 March 2023) was a Hungarian mathematician who specialized in number theory and combinatorics.

He was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory.

In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.

In combinatorial mathematics, the Bell numbers count the possible partitions of a set.

In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position.

In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of S.

In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.

In combinatorial mathematics, Baranyai's theorem (proved by and named after Zsolt Baranyai) deals with the decompositions of complete hypergraphs.

In combinatorial mathematics, an Aztec diamond of order n consists of all squares of a square lattice whose centers (x,y) satisfy |x| + |y| ≤ n.

It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published it in 1972.

Sequences satisfying Gauss congruence naturally occur in the study of topological dynamics, algebraic number theory and combinatorics.

The Lambek-Moser theorem belongs to combinatorial number theory.

They have applications in many areas of mathematics, including Galois theory, invariant theory, group theory, combinatorics, as well as further applications outside mathematics, including general relativity.

It is useful in combinatorics, for instance, in the enumeration of trees.

Discrete Mathematics Combinatorics

of subsets that satisfy certain prescribed conditions in combinatorial mathematics. Outlined by Ronald Fisher, a population

The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored

is a mathematical theorem in an area of mathematics called Ramsey theory.

In mathematics, the falling factorial (sometimes called the descending factorial, falling

Alfréd Rényi was a Hungarian mathematician who worked in probability theory, combinatorics, graph theory and number theory.

Eugène Catalan was a Belgian mathematician who defined the numbers called after him, while considering the solution of the problem of dissecting a polygon into triangles by means of non-intersecting diagonals.

George Szekeres was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics.

It is certainly for this last work on recreational mathematics that Ozanam will be most remembered.