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arXiv · 1911.04984

Permutations in two dimensions that maximally separate neighbors

Mohammed Albow·Jeff Edgington·Mario Lopez·Petr Vojtěchovský
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Abstract

We characterize all permutations on even-by-even grids that maximally separate neighboring vertices. More precisely, let $n_1$, $n_2$ be positive even integers, let $I(n_1,n_2)=\{1,\dots,n_1\}\times\{1,\dots,n_2\}$ be the $n_1\times n_2$ grid, let $d$ be the $L_1$ metric on $I(n_1,n_2)$, and let $N=\{\{x,y\}\in I(n_1,n_2)\times I(n_1,n_2):d(x,y)=1\}$ be the set of neighbors in $I(n_1,n_2)$. We characterize all permutations $π$ of $I(n_1,n_2)$ that maximize $\sum_{\{x,y\}\in N} d(π(x),π(y))$.

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Mohammed Albow, Jeff Edgington, Mario Lopez, Petr Vojtěchovský. 2019-11-12. Permutations in two dimensions that maximally separate neighbors. https://arxiv.org/abs/1911.04984

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