Unavoidable patterns in colored integers
Dr. Maria Axenovich
Iowa State University

Abstract:

Van der Waerden's theorem states that for any k, c there an N such that no matter how the integers in {1,2,...,N} are assigned c colors, there is a monochromatic arithmetic progression of length k.

In this talk, after a general introduction into Ramsey-type problems, I will discuss a "dual" problem of finding totally multicolored arithmetic progressions in colored integers. In particular, I will provide the conditions on the color classes forcing the presence of totally multicolored arithmetic progression. This is a joint work with Dimitri Fon-der-Flaass and Ryan Martin