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1 Faculty of Civil Engineering Rijeka

Abstract : This work is concerned with the perimeter enumeration of column-convex polyominoes. We consider both the rectangular lattice and the hexagonal lattice. For the rectangular lattice, two formulas for the generating function gf already exist and, to all appearances, neither of them admits of a further simplification. We first rederive those two formulas so as to make the paper self-contained, and then we enrich the rectangular lattice gf with some additional variables. That done, we make a change of variables, which practically produces the hexagonal lattice gf. This latter gf was first found by Lin and Wu in 1990. However, our present formula, in addition to having a simpler form, also allows a substantially easier Taylor series expansion. As to the methods, our one is descended from algebraic languages, whereas Lin and Wu used the Temperley methodology.

Author: Svjetlan Feretić -

Source: https://hal.archives-ouvertes.fr/


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