2022/01/03 by Helmut Prodinger, Prodinger, Helmut
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2201.00640
openalex publication_date 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Skew Dyck paths are a variation of Dyck paths, where additionally to steps (1,1) and (1,-1) a south-west step (-1,-1) is also allowed, provided that the path does not intersect itself. Replacing the south-west step by a red south-east step, we end up with decorated Dyck paths. Sequence A128723 of the Encyclopedia of Integer Sequences considers such paths where peaks at level 1 are forbidden. We provide a thorough analysis of a more general scenario, namely partial decorated Dyck paths, ending on a prescribed level j, both from left-to-right and from right-to-left (decorated Dyck paths are not symmetric). The approach is completely based on generating functions.