Periodic lozenge tilings of the plane

Details Periodic lozenge tilings of the plane Periodic lozenge tilings of the plane

2010-02-12

arxiv.org/abs/1002.2555v1

Mathematics

Combinatorics

17 pages

Scientific paper

This article addresses the problem of enumerating the tilings of a plane by lozenges, under the restriction that these tilings be doubly periodic. Kasteleyn's Pfaffian method is applied to compute the generating function of those permutations. The monomials of this function represent the different types of tilings, grouping them according to the number of lozenges in each orientation. We present an alternative approach to compute these types. Finally, two additional classes of tilings are proposed as open enumeration problems.

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