From Dyck paths to standard Young tableaux
Combinatorics
2022-03-15 v3
Abstract
We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength that is shown to be in bijection with the set of all SYT with boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some sense is dual to the known class of noncrossing partitions.
Keywords
Cite
@article{arxiv.1708.00513,
title = {From Dyck paths to standard Young tableaux},
author = {Juan B. Gil and Peter R. W. McNamara and Jordan O. Tirrell and Michael D. Weiner},
journal= {arXiv preprint arXiv:1708.00513},
year = {2022}
}
Comments
21 pages. Final version. To appear in Annals of Combinatorics