Mathematics > Combinatorics
[Submitted on 24 Apr 2018 (v1), last revised 21 Nov 2018 (this version, v2)]
Title:A lower bound for the $k$-multicolored sum-free problem in $\mathbb{Z}^n_m$
View PDFAbstract:In this paper, we give a lower bound for the maximum size of a $k$-colored sum-free set in $\mathbb{Z}_m^n$, where $k\geq 3$ and $m\geq 2$ are fixed and $n$ tends to infinity. If $m$ is a prime power, this lower bound matches (up to lower order terms) the previously known upper bound for the maximum size of a $k$-colored sum-free set in $\mathbb{Z}_m^n$. This generalizes a result of Kleinberg-Sawin-Speyer for the case $k=3$ and as part of our proof we also generalize a result by Pebody that was used in the work of Kleinberg-Sawin-Speyer. Both of these generalizations require several key new ideas.
Submission history
From: László Miklós Lovász [view email][v1] Tue, 24 Apr 2018 04:25:39 UTC (38 KB)
[v2] Wed, 21 Nov 2018 19:44:08 UTC (39 KB)
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