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arXiv · 1804.01293

Enumeration of Łukasiewicz paths modulo some patterns

Jean-Luc Baril·Sergey Kirgizov·Armen Petrossian
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Abstract

For any pattern $α$ of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length $n\geq 0$ 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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Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian. 2018-04-04. Enumeration of Łukasiewicz paths modulo some patterns. https://arxiv.org/abs/1804.01293

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