Dyck paths with catastrophes modulo the positions of a given pattern

Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian

Published 2022-02-23Version 1

For any pattern $p$ of length at most two, we provide generating functions and asymptotic approximations for the number of $p$-equivalence classes of Dyck paths with catastrophes, where two paths of the same length are $p$-equivalent whenever the positions of the occurrences of the pattern $p$ are the same.