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arXiv · 2305.04544

Maximal Arrangement of Dominos in the Diamond

Dominique Désérable·Rolf Hoffmann·Franciszek Seredyński
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Abstract

"Dominos" are special entities consisting of a hard dimer-like kernel surrounded by a soft hull and governed by local interactions. "Soft hull" and "hard kernel" mean that the hulls can overlap while the kernel acts under a repulsive potential. Unlike the dimer problem in statistical physics, which lists the number of all possible configurations for a given n x n lattice, the more modest goal herein is to provide lower and upper bounds for the maximum allowed number of dominos in the diamond. In this NP problem, a deterministic construction rule is proposed and leads to a suboptimal solution ψ_n as a lower bound. A certain disorder is then injected and leads to an upper bound ψ_n_upper reachable or not. In some cases, the lower and upper bounds coincide, so ψ_n = ψ_n_upper becomes the exact number of dominos for a maximum configuration.

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Dominique Désérable, Rolf Hoffmann, Franciszek Seredyński. 2023-05-08. Maximal Arrangement of Dominos in the Diamond. https://arxiv.org/abs/2305.04544

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