Geodesic
Maximum \(k\)-sum \(\mathbf{n}\)-free sets of the 2-dimensional integer lattice
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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For a positive integer $n$, let $[n]$ denote $\{1, \ldots, n\}$. For a 2-dimensional integer lattice point $\mathbf{b}$ and positive integers $k\geq 2$ and $n$, a $k$-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 $k\geq 2$ 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.
DOI : 10.37236/8895
Classification : 11B75, 11B30, 05D05
Mots-clés : sum-free sets

Ilkyoo Choi    ; Ringi Kim  1   ; Boram Park 

1 KAIST 
@article{10_37236_8895,
     author = {Ilkyoo Choi and Ringi Kim and Boram Park},
     title = {Maximum \(k\)-sum \(\mathbf{n}\)-free sets of the 2-dimensional integer lattice},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/8895},
     zbl = {1483.11039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8895/}
}
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Ilkyoo Choi; Ringi Kim; Boram Park. Maximum \(k\)-sum \(\mathbf{n}\)-free sets of the 2-dimensional integer lattice. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/8895

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