Avoiding a star of three-term arthmetic progressions

Masato Mimura, Norihide Tokushige

Published 2019-09-23Version 1

We provide an upper bound of the size of a subset A of F_p^n that does not admit a k-star of 3-APs (three-term arithmetic progressions). Namely, the subset A is assumed to contain no configuration of k 3-APs, sharing the middle term, such that all 2k+1 terms are distinct. In the proof, we adapt a new method in the recent work of Sauermann.