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arXiv · 1612.03759

Generating series of Periodic Parallelogram polyominoes

Jean Christophe Aval·Adrien Boussicault·Patxi Laborde-Zubieta·Mathias Pétréolle
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Abstract

The aim of this work is the study of the class of periodic parallelogram polyominoes, and two of its variantes. These objets are related to 321-avoiding affine permutations. We first provide a bijection with the set of triangles under Dyck paths. We then prove the ultimate periodicity of the generating series of our objects, and introduced a notion of primitive polyominoes, which we enumerate. We conclude by an asymptotic analysis.

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Jean Christophe Aval, Adrien Boussicault, Patxi Laborde-Zubieta, Mathias Pétréolle. 2016-12-12. Generating series of Periodic Parallelogram polyominoes. https://arxiv.org/abs/1612.03759

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