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}
}