Partial Skew Dyck Paths: A Kernel Method Approach

Skew Dyck paths are a variation of Dyck paths, where additionally to steps (1, 1) and ( 1 , - 1 ) a south–west step ( - 1 , - 1 ) 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. We analyze...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 38; no. 5
Main Author Prodinger, Helmut
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.10.2022
Springer Nature B.V
Subjects
Combinatorics
Engineering Design
Kernels
Mathematics
Mathematics and Statistics
Original Paper
05A19
Decorated Dyck paths
05A15
Skew Dyck paths
Generating functions
Kernel method
Online AccessGet full text
ISSN0911-0119
1435-5914
DOI10.1007/s00373-022-02541-8

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Summary:Skew Dyck paths are a variation of Dyck paths, where additionally to steps (1, 1) and ( 1 , - 1 ) a south–west step ( - 1 , - 1 ) 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. We analyze partial versions of them where the path ends on a fixed level j , not necessarily at level 0. We exclusively use generating functions and derive them with the celebrated kernel method.
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-022-02541-8