2023/05/08 by Dominique Désérable, Désérable, Dominique, Rolf Hoffmann +3 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #05B40 #68Q80 #82B20 #Combinatorics (math.CO) #FOS: Mathematics #Mass Spectrometry Techniques and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2305.04544
openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
"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 ψn as a lower bound. A certain disorder is then injected and leads to an upper bound ψnupper reachable or not. In some cases, the lower and upper bounds coincide, so ψn = ψnupper becomes the exact number of dominos for a maximum configuration.