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  1. Home > Articles & Issues >
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  3. The height of skew D ...
Article

The height of skew Dyck paths with two variants of downsteps

Helmut Prodinger ORCID (1) (2)
(1) Stellenbosch University [SU]
(2) National Institute for Theoretical and Computational Sciences
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Submitted on
February 14, 2026
Accepted on
July 14, 2026
Published on
July 23, 2026
Last modified on
July 23, 2026
Volume 28
vol. 28:3
Combinatorics
DOI
10.46298/dmtcs.17510
License
Attribution 4.0 International (CC BY 4.0)
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The height of skew Dyck paths with two variants of downsteps

Helmut Prodinger ORCID (1) (2)
(1) Stellenbosch University [SU]
(2) National Institute for Theoretical and Computational Sciences
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 $\sqrt n$. Suggestions by two reviewers are included. Third version contains some formatting
Keywords
  • Combinatorics
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