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

Abstract

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 $\gamma\approx 0.926$.

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Authors

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