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.
William Thomas TutteOC FRS FRSC was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a major Nazi German cipher system which was used for top-secret communications within the Wehrmacht High Command. The high-level, strategic nature of the intelligence obtained from Tutte's crucial breakthrough, in the bulk decrypting of Lorenz-enciphered messages specifically, contributed greatly, and perhaps even decisively, to the defeat of Nazi Germany. He also had a number of significant mathematical accomplishments, including foundation work in the fields of graph theory and matroid theory.
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 since 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.
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.
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. Some authors write Wn to denote a wheel graph with n vertices ; other authors instead use Wn to denote a wheel graph with n + 1 vertices, which is formed by connecting a single vertex to all vertices of a cycle of length n. The rest of this article uses the former notation.
The Mathematical Institute is the mathematics department at the University of Oxford in England. It is one of the nine departments of the university's Mathematical, Physical and Life Sciences Division. The institute includes both pure and applied mathematics and is one of the largest mathematics departments in the United Kingdom with about 200 academic staff. It was ranked as the top mathematics department in the UK in the 2021 Research Excellence Framework. Research at the Mathematical Institute covers all branches of mathematical sciences ranging from, for example, algebra, number theory, and geometry to the application of mathematics to a wide range of fields including industry, finance, networks, and the brain. It has more than 850 undergraduates and 550 doctoral or masters students. The institute inhabits a purpose-built building between Somerville College and Green Templeton College on Woodstock Road, next to the Faculty of Philosophy.
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.
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.
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.
Jon Hal Folkman was an American mathematician, a student of John Milnor, and a researcher at the RAND Corporation.
Leonid Mirsky was a Russian-British mathematician who worked in number theory, linear algebra, and combinatorics. Mirsky's theorem is named after him.
James Anthony Dominic Welsh was an English mathematician and emeritus professor of Oxford University's Mathematical Institute. He was an expert in matroid theory, the computational complexity of combinatorial enumeration problems, percolation theory, and cryptography.
William G. Brown is a Canadian mathematician specializing in graph theory. He is a professor emeritus of mathematics at McGill University.
