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.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Herbert Saul Wilf was an American mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He wrote numerous books and research papers. Together with Neil Calkin he founded The Electronic Journal of Combinatorics in 1994 and was its editor-in-chief until 2001.
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.
Jaroslav "Jarik" Nešetřil is a Czech mathematician, working at Charles University in Prague. His research areas include combinatorics, graph theory, algebra, posets, computer science.
Pierre Rosenstiehl was a French mathematician recognized for his work in graph theory, planar graphs, and graph drawing.
Carsten Thomassen is a Danish mathematician. He has been a Professor of Mathematics at the Technical University of Denmark since 1981, and since 1990 a member of the Royal Danish Academy of Sciences and Letters. His research concerns discrete mathematics and more specifically graph theory.
Václav (Vašek) Chvátal is a Professor Emeritus in the Department of Computer Science and Software Engineering at Concordia University in Montreal, Quebec, Canada, and a visiting professor at Charles University in Prague. He has published extensively on topics in graph theory, combinatorics, and combinatorial optimization.
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
The mathematical discipline of topological combinatorics is the application of topological and algebro-topological methods to solving problems in combinatorics.
János Pach is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.
Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.
Vojtěch Rödl is a Czech American mathematician, Samuel Candler Dobbs Professor at Emory University. He is noted for his contributions mainly to combinatorics having authored hundreds of research papers.
Charles Joseph Colbourn is a Canadian computer scientist and mathematician, whose research concerns graph algorithms, combinatorial designs, and their applications. From 1996 to 2001 he was the Dorothean Professor of Computer Science at the University of Vermont; since then he has been a professor of Computer Science and Engineering at Arizona State University.
The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications. The prize was first awarded at Eurocomb 2003 in Prague. Recipients must not be older than 35. The most recent prize was awarded at Eurocomb 2023 in Prague.
David Conlon is an Irish mathematician who is a Professor of Mathematics at the California Institute of Technology. His research interests are in Hungarian-style combinatorics, particularly Ramsey theory, extremal graph theory, combinatorial number theory, and probabilistic methods in combinatorics. He proved the first superpolynomial improvement on the Erdős–Szekeres bound on diagonal Ramsey numbers. He won the European Prize in Combinatorics in 2011 for his work in Ramsey theory and for his progress on Sidorenko's conjecture, and the Whitehead Prize in 2019.
Dmitry Feichtner-Kozlov is a Russian-German mathematician.
Martin Grötschel is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research. From 1991 to 2012 he was Vice President of the Zuse Institute Berlin (ZIB) and served from 2012 to 2015 as ZIB's President. From 2015 to 2020 he was President of the Berlin-Brandenburg Academy of Sciences and Humanities (BBAW).
David Ronald Wood is a Professor in the School of Mathematics at Monash University in Melbourne, Australia. His research area is discrete mathematics and theoretical computer science, especially structural graph theory, extremal graph theory, geometric graph theory, graph colouring, graph drawing, and combinatorial geometry.
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