Domino Tilings with One Diagonal Impurity

Issue title: Lattice Path Combinatorics and Applications

Article type: Research Article

Authors: Nakano, Fumihiko | Sadahiro, Taizo

Affiliations: Department of Mathematics, Gakushuin University, Tokyo, 171-8588, Japan, [email protected] | Department of Computer Science, Tsuda College, Tokyo 187-8577, Japan, [email protected]

Note: [] Address for correspondence: Tsuda-machi 2-1-1 Kodaira, Tokyo, Japan

Abstract: This paper studies the dimer model on the dual graph of the square-octagon lattice, which can be viewed as the domino tilings with impurities in some sense. In particular, under a certain boundary condition where only one impurity is contained, we give an exact formula representing the probability of finding an impurity at a given site in a uniformly random dimer configuration in terms of simple random walks on the square lattice.

DOI: 10.3233/FI-2012-699

Journal: Fundamenta Informaticae, vol. 117, no. 1-4, pp. 249-264, 2012