Standard Young Tableaux and Colored Motzkin Paths

Sen-Peng Eu, Tung-Shan Fu, Justin T. Hou, Te-Wei Hsu

Published 2013-02-13Version 1

In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows and the set of SYTs with at most 2d rows.