On \({k}\)-Dyck Paths with a Negative Boundary

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 31 Mar 2024Embargo end date: 01 Jan 2019Publisher:Combinatorial PressJournal:Journal of Combinatorial Mathematics and Combinatorial Computing, volume 119, pages 3-12 (issn: 0835-3026, eissn: 2817-576X,

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Authors: Prodinger, Helmut;

doi: 10.61091/jcmcc119-01 , 10.48550/arxiv.1912.06930

arXiv: 1912.06930

On \({k}\)-Dyck Paths with a Negative Boundary

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Abstract

Paths that consist of up-steps of one unit and down-steps of \(k\) units, being bounded below by a horizontal line \(-t\), behave like \(t+1\) ordered tuples of \(k\)-Dyck paths, provided that \(t\le k\). We describe the general case, allowing \(t\) also to be larger. Arguments are bijective and/or analytic.

Related Organizations

Stellenbosch University
South Africa

Keywords

\(k\)-Dyck paths, generating functions, Exact enumeration problems, generating functions, bijections, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Paths and cycles, Trees

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