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

TL;DR

This paper introduces a new bijection linking stacked directed polyominoes and Motzkin paths with alternative catastrophes, enhancing understanding of their combinatorial parameters.

Contribution

It establishes a novel bijection between these two combinatorial structures, providing new insights into their properties and relationships.

Findings

New bijection between stacked directed polyominoes and Motzkin paths

Improved understanding of parameters of stacked directed animals

Potential applications in combinatorial enumeration

Abstract

We present a novel bijection between stacked directed polyominoes and Motzkin paths with alternative catastrophes. Further, we show how this new connection can be used in order to obtain a better understanding of certain parameters of stacked directed animals.