4 papers · 1 filter
The height of Dyck paths and checkerboard labellings
Helmut Prodinger
Dyck paths and certain black/white labelling of nodes leads to the \emph{white-height}. Using generating functions and tricks of the trade, we establish that the average white-heig…
The height of skew Dyck paths with two variants of downsteps
Helmut Prodinger
Recently, in the context of walks of hexagonal circle packings, interest has emerged in the family of skew Dyck paths with two variants of down-steps. These paths have steps $U, D_…
Skew 2-Dyck paths via the kernel method
Helmut Prodinger
We continue on a recent concept introduced by Kariuki and Okoth, about skew 2-Dyck paths, introducing an additional down-step , together with the usual steps (up) and do…
Prefixes of Stanley's Catalan paths with odd returns to the -axis -- standard version and skew Catalan-Stanley paths
Helmut Prodinger
Stanley considered Dyck paths where each maximal run of down-steps to the -axis has odd length; they are also enumerated by (shifted) Catalan numbers. Prefixes of these combinat…