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Combinatorics

Combinatorics concerns the study of discrete objects. It has applications to diverse areas of mathematics and science, and has played a particularly important role in the development of computer science. 

While it is arguably as old as counting, combinatorics has grown remarkably in the past half century alongside the rise of computers. It borrows tools from diverse areas of mathematics. Examples include the probabilistic method, which was pioneered by Paul Erdös and uses probability to prove the existence of combinatorial structures with interesting properties, algebraic methods such as in the use of algebraic geometry to solve problems in discrete geometry and extremal graph theory, and topological methods beginning with Lovász’ proof of the Kneser conjecture. A notable application in number theory is in the proof of the Green-Tao theorem that there are arbitrarily long arithmetic progressions of primes. The Stanford Mathematics department is a leader in combinatorics, with particular strengths in probabilistic combinatorics, extremal combinatorics, algebraic combinatorics, additive combinatorics, combinatorial geometry, and applications to computer science.

Faculty

Szegö Assistant Professor
  650-723-4507
  Building 380, 382-Q2
Mary V. Sunseri Professor of Statistics and Mathematics
  (650) 723-5183
  Building 380, 383-D
  (650) 736-6988
  Building 380, 383-K
Anne T. and Robert M. Bass Professor of the School of Humanities and Sciences
  (650) 723-2629
  Building 380, 383-W
Stanford Science Fellow
  384-D
  (650) 724-6001
  Building 380, 383-J