A Bijection Between Weighted Dyck Paths and 1234-avoiding Up-Down Permutations
Justine Falque
TL;DR
This paper establishes a structural bijection between 1234-avoiding up-down permutations and weighted Dyck paths, providing a new combinatorial correspondence for three-dimensional Catalan objects.
Contribution
It introduces a novel bijection connecting two complex three-dimensional Catalan structures, enriching the combinatorial understanding of these objects.
Findings
Bijection between 1234-avoiding up-down permutations and weighted Dyck paths
New combinatorial interpretation of three-dimensional Catalan numbers
Enhanced understanding of structural properties of these objects
Abstract
Three-dimensional Catalan numbers are a variant of the classical (bidimensional) Catalan numbers, that count, among other interesting objects, the standard Young tableaux of shape (n,n,n). In this paper, we present a structural bijection between two three-dimensional Catalan objects: 1234-avoiding up-down permutations, and a class of weighted Dyck paths.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Geometric and Algebraic Topology