Bounds on sizes of general caps in AG(n,q) via the Croot-Lev-Pach polynomial method

2018/06/13 by Bennett, Michael
#51E22 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05303

Abstract

In 2016, Ellenberg and Gijswijt employed a method of Croot, Lev, and Pach to show that a maximal cap in AG(n, q) has size O(q^cn) for some c < 1. In this paper, we show more generally that if S is a subset of AG(n, q) containing no m points on any (m - 2)- flat, then |S| < q^c_mn for some c_m < 1, as long as q is odd or m is even.

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