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.
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.
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.
The no-three-in-line problem in discrete geometry asks how many points can be placed in the grid so that no three points lie on the same line. The problem concerns lines of all slopes, not only those aligned with the grid. It was introduced by Henry Dudeney in 1900. Brass, Moser, and Pach call it "one of the oldest and most extensively studied geometric questions concerning lattice points".
Jaroslav "Jarik" Nešetřil is a Czech mathematician, working at Charles University in Prague. His research areas include combinatorics, graph theory, algebra, posets, computer science.
In graph theory, boxicity is a graph invariant, introduced by Fred S. Roberts in 1969.
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they come from pairs of vertices in the factor graphs that are either adjacent or identical. The strong product is one of several different graph product operations that have been studied in graph theory. The strong product of any two graphs can be constructed as the union of two other products of the same two graphs, the Cartesian product of graphs and the tensor product of graphs.
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.
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
Richard M. Pollack was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus until his death.
In graph drawing and geometric graph theory, the slope number of a graph is the minimum possible number of distinct slopes of edges in a drawing of the graph in which vertices are represented as points in the Euclidean plane and edges are represented as line segments that do not pass through any non-incident vertex.
In the mathematical field of graph theory, the queue number of a graph is a graph invariant defined analogously to stack number using first-in first-out (queue) orderings in place of last-in first-out (stack) orderings.
Isabel Alicia Hubard Escalera is a Mexican mathematician in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM).
Ian Murray Wanless is an Australian mathematician. He is a professor in the School of Mathematics at Monash University in Melbourne, Australia. His research area is combinatorics, principally Latin squares, graph theory and matrix permanents.
In graph theory, a -bounded family of graphs is one for which there is some function such that, for every integer the graphs in with can be colored with at most colors. The function is called a -binding function for . These concepts and their notations were formulated by András Gyárfás. The use of the Greek letter chi in the term -bounded is based on the fact that the chromatic number of a graph is commonly denoted . An overview of the area can be found in a survey of Alex Scott and Paul Seymour.
Catherine Greenhill is an Australian mathematician known for her research on random graphs, combinatorial enumeration and Markov chains. She is a professor of mathematics in the School of Mathematics and Statistics at the University of New South Wales, and an editor-in-chief of the Electronic Journal of Combinatorics.
