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arXiv · 1611.03766

Periodic Parallelogram Polyominoes

Adrien Boussicault·Patxi Laborde-Zubieta
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Abstract

A periodic parallelogram polyomino is a parallelogram polyomino such that we glue the first and the last column. In this work we extend a bijection between ordered trees and parallelogram polyominoes in order to compute the generating function of periodic parallelogram polyominoes with respect to the height, the width and the intrinsic thickness, a new statistic unrelated to the existing statistics on parallelogram polyominoes. Moreover we define a rotation over periodic parallelogram polyominoes, which induces a partitioning in equivalent classes called strips. We also compute the generating function of strips using the theory of Pólya.

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Adrien Boussicault, Patxi Laborde-Zubieta. 2016-11-11. Periodic Parallelogram Polyominoes. https://arxiv.org/abs/1611.03766

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