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.
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.
Ding Shisun was a Chinese mathematician, academic administrator, and politician. He served as president of Peking University during the 1989 Tiananmen Square protests and massacre and was forced to resign afterwards. He later served as chairman of the China Democratic League from 1996 to 2005 and a vice chairperson of the Standing Committee of the National People's Congress.
The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.
Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
Henry Wadsworth Gould is a Professor Emeritus of Mathematics at West Virginia University.
Rodica Eugenia Simion was a Romanian-American mathematician. She was the Columbian School Professor of Mathematics at George Washington University. Her research concerned combinatorics: she was a pioneer in the study of permutation patterns, and an expert on noncrossing partitions.
In combinatorics, a lattice pathL in the d-dimensional integer lattice of length k with steps in the set S, is a sequence of vectors such that each consecutive difference lies in S. A lattice path may lie in any lattice in , but the integer lattice is most commonly used.
Analytic Combinatorics is a book on the mathematics of combinatorial enumeration, using generating functions and complex analysis to understand the growth rates of the numbers of combinatorial objects. It was written by Philippe Flajolet and Robert Sedgewick, and published by the Cambridge University Press in 2009. It won the Leroy P. Steele Prize in 2019.
Lu Jiaxi was a self-taught Chinese mathematician who made important contributions in combinatorial design theory. He was a high school physics teacher in a remote city and worked in his spare time on the problem of large sets of disjoint Steiner triple systems.
Xu Lizhi, better known as Leetsch Charles Hsu, was a Chinese mathematician and educator. He co-founded the Department of Mathematics of Jilin University and founded the Institute of Applied Mathematics and the Journal of Mathematical Research with Applications at the Dalian University of Technology. Together with American mathematician Henry W. Gould, he established the Gould–Hsu Matrix Inversion Formula in 1973.
Lynne Marie Butler is an American mathematician whose research interests include algebraic combinatorics, group theory, and mathematical statistics. She is a professor of mathematics at Haverford College.
Wu Shuqing was a Chinese economist and educator. He was president of Peking University from August 1989 to August 1996 and vice-president of Renmin University of China.
Dihua Jiang is a Chinese-born American mathematician. He is a professor of mathematics at the University of Minnesota working in number theory, automorphic forms, and the Langlands program.
The Philippe Flajolet Lecture Prize is awarded to for contributions to analytic combinatorics and analysis of algorithms, in the fields of theoretical computer science. This prize is named in memory of Philippe Flajolet.
Jiang Boju is a Chinese mathematician and a professor of Peking University, School of Mathematical Sciences. He is known for his contributions to topology.
James Haglund is an American mathematician who specializes in algebraic combinatorics and enumerative combinatorics, and works as a professor of mathematics at the University of Pennsylvania.
