Inversion relations, reciprocity and polyominoes

Details Inversion relations, reciprocity and polyominoes Inversion relations, reciprocity and polyominoes

1999-08-23

arxiv.org/abs/math/9908123v1

Mathematics

Combinatorics

32 pages, 7 figures

Scientific paper

We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a connection between the reciprocity results known to combinatorialists and the inversion relations used by physicists to solve models in statistical mechanics. For several classes of convex polygons, the inversion (reciprocity) relation, augmented by certain symmetry and analyticity properties, completely determines the anisotropic perimeter generating function.

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