Entropy of full covering of the kagome lattice by straight trimers

Abstract

We consider the number of ways all the sites of a kagome lattice can be covered by non-overlapping linear rigid rods where each rod covers 3 sites. We establish a 2-to-1 correspondence between the configurations of trimers on the kagome lattice to the covering by dimers of a related hexagonal lattice to show that entropy of coverings per trimer $s_{\text{tri,kag}}$ equals the entropy per dimer $s_{\text{dim,hex}}$, and is given by $s_{\text{tri,kag}}=s_{\text{dim,hex}}=\frac{1}{2\pi }{\int }_0^{2\pi /3}\log (2+2\cos k)dk\approx 0.323065947\dots$.

9 pages, 8 figures, 1 table