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

초록

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 k-sum b-free set of [n] x [n] is a subset S of [n] x [n] such that there are no elements a(1), ..., a(k) in S satisfying a(1) + ... + 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] x [n]. This is the first investigation of the non-homogeneous sum-free set problem in higher dimensions.

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