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.
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