The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
Statistical Mechanics
2009-11-11 v1 Combinatorics
Abstract
We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.
Cite
@article{arxiv.cond-mat/0607647,
title = {The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary},
author = {F. Y. Wu},
journal= {arXiv preprint arXiv:cond-mat/0607647},
year = {2009}
}
Comments
4 Pages to appear in the Physical Review E (2006)