Affiliation: Department of Physics, Northeastern University, Boston
Email: fywu@neu.edu
Title Of Talk: Some recent results in dimer statistics
Abstract: This talk reviews some recent new results on close-packed dimers (dominoes) on planar and nonorientable surfaces. We deduce closed-form expressions for dimer generating functions on the Moebius strip and the Klein bottle. The expressions depend explicitly on whether the linear sizes of the lattice being even or odd, and are given in the form of double products and also in terms of generalized Fibonacci numbers. The solutions lead to an extension of the Stanley-Propp reciprocity relation for dimer enumerations and several curious identities connecting results for different embedding lattices. Using a vertex model formulation we deduce solutions for several two-dimensional regular arrays including the triangular, kagome, and the Union-Jack lattices. We also deduce the generating function for close-packed dimers on a rectangular net with a boundary defect.
Last update made Wed Feb 12 18:53:55 EST 2003.
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