Séminaire Lotharingien de Combinatoire, 85B.71 (2021), 12 pp.
Justine Falque
A Bijection Between Weighted Dyck Paths and 1234-Avoiding Alternating Permutations
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, statistics-preserving bijection between two three-dimensional
Catalan objects:
1234-avoiding alternating permutations, and a class of weighted Dyck paths.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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