Skew Dyck paths having no peaks at level 1
Combinatorics
2022-01-26 v1
Abstract
Skew Dyck paths are a variation of Dyck paths, where additionally to steps and a south-west step 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 , both from left-to-right and from right-to-left (decorated Dyck paths are not symmetric). The approach is completely based on generating functions.
Keywords
Cite
@article{arxiv.2201.00640,
title = {Skew Dyck paths having no peaks at level 1},
author = {Helmut Prodinger},
journal= {arXiv preprint arXiv:2201.00640},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2111.14797