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.
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
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.
Richard Rado FRS was a German-born British mathematician whose research concerned combinatorics and graph theory. He was Jewish and left Germany to escape Nazi persecution. He earned two PhDs: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to study at Cambridge. After he was awarded the scholarship, Rado and his wife left for the UK in 1933. He was appointed Professor of Mathematics at the University of Reading in 1954 and remained there until he retired in 1971.
Endre Szemerédi is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science at Rutgers University since 1986. He also holds a professor emeritus status at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences.
Euclid and His Modern Rivals is a mathematical book published in 1879 by the English mathematician Charles Lutwidge Dodgson (1832–1898), better known under his literary pseudonym "Lewis Carroll". It considers the pedagogic merit of thirteen contemporary geometry textbooks, demonstrating how each in turn is either inferior to or functionally identical to Euclid's Elements.
Paul D. Seymour is a British mathematician known for his work in discrete mathematics, especially graph theory. He was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs, χ-boundedness, and the Erdős–Hajnal conjecture. Many of his recent papers are available from his website.
László Lovász is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He was the president of the International Mathematical Union from 2007 to 2010 and the president of the Hungarian Academy of Sciences from 2014 to 2020.
In the mathematical discipline of graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can also be defined as the 1-skeleton of an (n – 1)-gonal pyramid.
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.
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.
Ronald Cedric Read was a British mathematician, latterly a professor emeritus of mathematics at the University of Waterloo, Canada. He published many books and papers, primarily on enumeration of graphs, graph isomorphism, chromatic polynomials, and particularly, the use of computers in graph-theoretical research. A majority of his later work was done in Waterloo. Read received his Ph.D. (1959) in graph theory from the University of London.
János Pach is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.
András Hajnal was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics.
Michel Marie Deza was a Soviet and French mathematician, specializing in combinatorics, discrete geometry and graph theory. He was the retired director of research at the French National Centre for Scientific Research (CNRS), the vice president of the European Academy of Sciences, a research professor at the Japan Advanced Institute of Science and Technology, and one of the three founding editors-in-chief of the European Journal of Combinatorics.
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.
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.
William G. Brown is a Canadian mathematician specializing in graph theory. He is a professor emeritus of mathematics at McGill University.
