A Bijection Between Weighted Dyck Paths and 1234-avoiding Up-Down Permutations

arXiv2012.00122MaRDI QIDQ6354944

Publication date: 30 November 2020

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.

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Combinatorial aspects of representation theory (05E10)

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