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- W2922085044 abstract "For a positive integer $n$, let $[n]$ denote ${1, ldots, n}$. For a 2-dimensional integer lattice point $mathbf{b}$ and positive integers $kgeq 2$ and $n$, a textit{$k$-sum $mathbf{b}$-free set} of $[n]times [n]$ is a subset $S$ of $[n]times [n]$ such that there are no elements ${mathbf{a}}_1, ldots, {mathbf{a}}_k$ in $S$ satisfying ${mathbf{a}}_1+cdots+{mathbf{a}}_k =mathbf{b}$. For a 2-dimensional integer lattice point $mathbf{b}$ and positive integers $kgeq 2$ and $n$, we determine the maximum density of a {$k$-sum $mathbf{b}$-free set} of $[n]times [n]$. This is the first investigation of the non-homogeneous sum-free set problem in higher dimensions." @default.
- W2922085044 created "2019-03-22" @default.
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- W2922085044 date "2019-03-11" @default.
- W2922085044 modified "2023-09-27" @default.
- W2922085044 title "Maximum $k$-sum $mathbf{n}$-free sets of the 2-dimensional integer lattice" @default.
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