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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