Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
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). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2, ..., n} then Sym(M) is usually denoted by Sn, and may be called the symmetric group on n letters.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
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 theorem in 1938, but did not publish it until 1961. It is part of the field of combinatorics, and one of the central results of extremal set theory.
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Béla Bollobás FRS is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul Erdős from the age of 14.
Czesław Ryll-Nardzewski was a Polish mathematician.
Ben Joseph Green FRS is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford.
Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other. Less obviously, polyhedral geometry plays a significant role.
Jacobus Hendricus ("Jack") van Lint was a Dutch mathematician, professor at the Eindhoven University of Technology, of which he was rector magnificus from 1991 till 1996.
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
Rosemary A. Bailey is a British statistician who works in the design of experiments and the analysis of variance and in related areas of combinatorial design, especially in association schemes. She has written books on the design of experiments, on association schemes, and on linear models in statistics.
In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism. Omega-categoricity is the special case κ = = ω of κ-categoricity, and omega-categorical theories are also referred to as ω-categorical. The notion is most important for countable first-order theories.
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
In the mathematical field of graph theory, the Schläfli graph, named after Ludwig Schläfli, is a 16-regular undirected graph with 27 vertices and 216 edges. It is a strongly regular graph with parameters srg(27, 16, 10, 8).
Leonid Mirsky was a Russian-British mathematician who worked in number theory, linear algebra, and combinatorics. Mirsky's theorem is named after him.
Combinatorial matrix theory is a branch of linear algebra and combinatorics that studies matrices in terms of the patterns of nonzeros and of positive and negative values in their coefficients.
Felix Adalbert Behrend was a German mathematician of Jewish descent who escaped Nazi Germany and settled in Australia. His research interests included combinatorics, number theory, and topology. Behrend's theorem and Behrend sequences are named after him.
Jan Saxl was a Czech-British mathematician, and a professor at the University of Cambridge. He was known for his work in finite group theory, particularly on consequences of the classification of finite simple groups.
Martin Liebeck is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics.
