English

Generating series of Periodic Parallelogram polyominoes

Combinatorics 2016-12-13 v1

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.

Keywords

Cite

@article{arxiv.1612.03759,
  title  = {Generating series of Periodic Parallelogram polyominoes},
  author = {Jean Christophe Aval and Adrien Boussicault and Patxi Laborde-Zubieta and Mathias Pétréolle},
  journal= {arXiv preprint arXiv:1612.03759},
  year   = {2016}
}

Comments

14 pages, 6 figures