Arithmetic Combinatorics

Combinatorics is concerned with counting problems. The theorems in the subject typically do not assume much structure and apply quite generally. Arithmetic is concerned with algebraic operations on the integers or in mathematical structures, called finite fields, and is usually a very structured study. The interplay between arithmetic and combinatorics has resulted in a number of striking results and a flurry of activity. Endre Szemerédi is one of the fathers of the subject.