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

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.

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

References in corpus (2)

• First order transition for the optimal search time of Lévy flights with resetting
• Lattice paths with catastrophes