**Combinatorics**

Faculty with research interests in combinatorics are Thái Hoàng Lê and Bing Wei.

Combinatorics is a branch of mathematics that deals with counting, arranging, and organizing objects. It focuses on discrete structures and the enumeration of possibilities. Combinatorics has applications in computer science, statistics, and various fields involving discrete choices and optimization.

Thái Hoàng Lê is interested in combinatorial questions taking place in a group, such as the integers, vector spaces over finite fields, and general (finite or infinite) abelian groups. To address these questions, tools from other areas of mathematics such as algebra (e.g. the polynomial method), analysis (e.g. Fourier analysis) and number theory are especially useful. For example, if a set A is large in some sense in a group, must it contain some pattern such as {x, y, x+y} or {x, x+y, x+2y}? The sumset of two sets A and B is the set of all possible sums a+b where a is an element of A and b is an element of B. A general principle says that sumsets have more structure than invidual sets, and he works on various instances of this principle.