English

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

Combinatorics 2020-12-02 v1 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.2012.00122,
  title  = {A Bijection Between Weighted Dyck Paths and 1234-avoiding Up-Down Permutations},
  author = {Justine Falque},
  journal= {arXiv preprint arXiv:2012.00122},
  year   = {2020}
}
R2 v1 2026-06-23T20:37:15.919Z