Dyck paths with catastrophes modulo the positions of a given pattern

02/23/2022

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by   Jean-Luc Baril, et al.

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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.