Dyck paths with catastrophes modulo the positions of a given pattern

Abstract

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.

25 pages, 14 figures, 1 table