Progression-free sets in $\mathbb Z_4^n$ are exponentially small


We show that for an integer $n\ge 1$, any subset $A\subseteq \mathbb{Z}_4^n$ free of three-term arithmetic progressions has size $|A|\le 4^{\gamma n}$, with an absolute constant $\gamma\approx 0.926$.


Ernie Croot

Georgia Institute of Technology, Atlanta, GA

Vsevolod F. Lev

The University of Haifa at Oranim, Tivon, Israel

Péter Pál Pach

Budapest University of Technology and Economics, Budapest, Hungary