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

Pages 331-337 from Volume 185 (2017), Issue 1 by Ernie Croot, Vsevolod F. Lev, Péter Pál Pach

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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Keywords
, , ,
Mathematical Subject Classification
Primary: Secondary: , , , ,
DOI
https://doi.org/10.4007/annals.2017.185.1.7
MR
3583357
zbMATH
06686589
Milestones
Received: 5 May 2016
Accepted: 8 September 2016
Published online: 2 December 2016

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