Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in 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 combinatorial mathematics, a Steiner system is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.
Fan-Rong King Chung Graham, known professionally as Fan Chung, is an American mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree distribution.
Raj Chandra Bose (or Basu) (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him. He also invented the notions of partial geometry, association scheme, and strongly regular graph and started a systematic study of difference sets to construct symmetric block designs. He was notable for his work along with S. S. Shrikhande and E. T. Parker in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that for no n do there exist two mutually orthogonal Latin squares of order 4n + 2.
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and the theory of error-correcting codes. In algebra, association schemes generalize groups, and the theory of association schemes generalizes the character theory of linear representations of groups.
Noga Alon is an Israeli mathematician and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers.
Thomas Penyngton Kirkman FRS was a British mathematician and ordained minister of the Church of England. Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by Alexander Macfarlane as one of ten leading 19th-century British mathematicians. In the 1840s, he obtained an existence theorem for Steiner triple systems that founded the field of combinatorial design theory, while the related Kirkman's schoolgirl problem is named after him.
Peter Jephson Cameron FRSE is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London.
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states:
Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast.
Sharadchandra Shankar Shrikhande was an Indian mathematician with notable achievements in combinatorial mathematics. He was notable for his breakthrough work along with R. C. Bose and E. T. Parker in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order 4n + 2 for any n. Shrikhande's specialties were combinatorics and statistical designs. The Shrikhande graph is used in statistical design.
The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, publishes a bulletin and awards a number of medals, including the Euler, Hall, Kirkman, and Stanton Medals. It is based in Duluth, Minnesota and its operation office is housed at University of Minnesota Duluth. The institute was minimally active between 2010 and 2016 and resumed its full activities in March 2016.
Richard Michael Wilson is a mathematician and a professor emeritus at the California Institute of Technology. Wilson and his PhD supervisor Dijen K. Ray-Chaudhuri, solved Kirkman's schoolgirl problem in 1968. Wilson is known for his work in combinatorial mathematics, as well as on historical flutes.
Ernest Tilden Parker (1926–1991) was a professor emeritus of the University of Illinois Urbana-Champaign. He is notable for his breakthrough work along with R. C. Bose and S. S. Shrikhande in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order for every . He was at that time employed in the UNIVAC division of Remington Rand, but he subsequently joined the mathematics faculty at t University of Illinois. In 1968, he and a Ph.D. student, K. B. Reid, disproved a conjecture on tournaments by Paul Erdős and Leo Moser.
Christopher David Godsil is a professor and the former Chair at the Department of Combinatorics and Optimization in the faculty of mathematics at the University of Waterloo. He wrote the popular textbook on algebraic graph theory, entitled Algebraic Graph Theory, with Gordon Royle, His earlier textbook on algebraic combinatorics discussed distance-regular graphs and association schemes.
Vitaly Bergelson is a mathematical researcher and professor at Ohio State University in Columbus, Ohio. His research focuses on ergodic theory and combinatorics.
Jeffry Ned Kahn is a professor of mathematics at Rutgers University notable for his work in combinatorics.
James William Peter Hirschfeld is an Australian mathematician, resident in the United Kingdom, specializing in combinatorial geometry and the geometry of finite fields. He is an emeritus professor and Tutorial Fellow at the University of Sussex.
Anne Schilling is an American mathematician specializing in algebraic combinatorics, representation theory, and mathematical physics. She is a professor of mathematics at the University of California, Davis.
József Balogh is a Hungarian-American mathematician, specializing in graph theory and combinatorics.
Ezra Abraham "Bud" Brown is an American mathematician active in combinatorics, algebraic number theory, elliptic curves, graph theory, expository mathematics and cryptography. He spent most of his career at Virginia Tech where he is now Alumni Distinguished Professor Emeritus of Mathematics.
