Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths
Jean-Luc Baril, Sergey Kirgizov
TL;DR
This paper constructs explicit bijections between Dyck and Motzkin meanders with catastrophes and pattern-avoiding Dyck paths, revealing new combinatorial correspondences and extending understanding of these structures.
Contribution
It introduces constructive bijections connecting meanders with catastrophes to pattern-avoiding Dyck paths, providing new combinatorial insights.
Findings
Bijections between Dyck/Motzkin meanders with catastrophes and pattern-avoiding Dyck paths
Correspondences from Dyck and Motzkin excursions to restricted Dyck paths
Enhanced understanding of combinatorial structures and their relationships
Abstract
In this note, we present constructive bijections from Dyck and Motzkin meanders with catastrophes to Dyck paths avoiding some patterns. As a byproduct, we deduce correspondences from Dyck and Motzkin excursions to restricted Dyck paths.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Topological and Geometric Data Analysis