Maximal Arrangement of Dominos in the Diamond

"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 {\psi}_n as a lower bound. A certain disorder is then injected and leads to an upper bound {\psi}_n_upper reachable or not. In some cases, the lower and upper bounds coincide, so {\psi}_n = {\psi}_n_upper becomes the exact number of dominos for a maximum configuration.