Entropy of full covering of the kagome lattice by straight trimers.

We consider the number of ways all the sites of a kagome lattice can be covered by nonoverlapping linear rigid rods where each rod covers three sites. We establish a two-to-one 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_{tri,kag} equals the entropy per dimer s_{dim,hex}, and is given by s_{tri,kag}=s_{dim,hex}=1/2π∫_{0}^{2π/3}ln(2+2cosk)dk≈0.323065947....