English

A Bijection between Stacked Directed Polyominoes and Motzkin Paths with Alternative Catastrophes

Combinatorics 2026-05-29 v2 Discrete Mathematics

Abstract

We present a novel bijection between stacked directed polyominoes and Motzkin paths with catastrophes. Further, we leverage this new bridge between these two worlds to obtain a better understanding of certain parameters of stacked directed animals. In particular, we obtain improved lower and upper bounds on the asymptotic width of stacked directed animals.

Keywords

Cite

@article{arxiv.2406.16417,
  title  = {A Bijection between Stacked Directed Polyominoes and Motzkin Paths with Alternative Catastrophes},
  author = {Florian Schager and Michael Wallner},
  journal= {arXiv preprint arXiv:2406.16417},
  year   = {2026}
}

Comments

extended version of the abstract in Proceedings GASCom 2024, arXiv:2406.14588