Maximum k-sum n-free sets of the 2-dimensional integer lattice

2019/03/11 by Choi, Ilkyoo, Kim, Ringi, Park, Boram
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.04132

Abstract

For a positive integer n, let [n] denote \1, …, n\. For a 2-dimensional integer lattice point b and positive integers k≥ 2 and n, a \textitk-sum b-free set of [n]× [n] is a subset S of [n]× [n] such that there are no elements a₁, …, a_k in S satisfying a₁+⋯+a_k =b. For a 2-dimensional integer lattice point b and positive integers k≥ 2 and n, we determine the maximum density of a k-sum b-free set of [n]× [n]. This is the first investigation of the non-homogeneous sum-free set problem in higher dimensions.

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