Enumeration of Łukasiewicz paths modulo some patterns

2018/04/04 by Baril, Jean-Luc, Kirgizov, Sergey, Petrossian, Armen
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.01293

Abstract

For any pattern α of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length n≥ 0 where two paths are equivalent whenever the occurrence positions of α are identical on these paths. As a byproduct, we give a constructive bijection between Motzkin paths and some equivalence classes of Łukasiewicz paths.

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