combinatorics

The height of skew Dyck paths with two variants of downsteps

arXiv:2601.10894 · doi:10.46298/dmtcs.17510

summary

The paper analyzes skew Dyck paths that include two different down‑step types, using generating functions, the kernel method, and linear systems to enumerate these paths and determine that their average height grows on the order of √n.

Abstract

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 $U, D_{g}, D_{b}, L = D_{r}$ . Using generating functions, the kernel method and (in)finite linear systems, contributions to the (average) height and other enumerations are made. As in many similar instances, the average height is of order $n$ .

Suggestions by two reviewers are included. Third version contains some formatting

Topics & keywords

#skew dyck paths #lattice path enumeration #generating functions #average height #kernel methodDyck pathdown-step variantsheight distributionkernel methodlinear systems