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Prefixes of Stanley's Catalan paths with odd returns to the x-axis -- standard version and skew Catalan-Stanley paths

2024/02/02 by Prodinger, Helmut
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.01429

Abstract

Stanley considered Dyck paths where each maximal run of down-steps to the x-axis has odd length; they are also enumerated by (shifted) Catalan numbers. Prefixes of these combinatorial objects are enumerated using the kernel method. A more challenging version of skew Dyck paths combined with Stanley's restriction is also considered.

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