The complexity of solution-free sets of integers for general linear equations

@article{Edwards2019TheCO,
  title={The complexity of solution-free sets of integers for general linear equations},
  author={Keith J. Edwards and Steven D. Noble},
  journal={Discret. Appl. Math.},
  year={2019},
  volume={270},
  pages={115-133}
}
Maximum k-sum n-free sets of the 2-dimensional integer lattice
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] × [n] is a subset S of [n] × [n] such
Maximum $k$-Sum $\mathbf{n}$-Free Sets of the 2-Dimensional Integer Lattice
TLDR
The maximum density of a $k$-sum $\mathbf{b}$-free set of $[n]\times [n]$ is determined, the first investigation of the non-homogeneous sum- free set problem in higher dimensions.

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