@article{06a6255f71c14a309460219ccc59da9a,
title = "Standard Young tableaux and colored Motzkin paths",
abstract = "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 2. d+. 1 rows and the set of SYTs with at most 2. d rows.",
keywords = "Bijection, Colored Motzkin paths, Shuffles of parenthesis systems, Standard Young tableaux",
author = "Eu, {Sen Peng} and Fu, {Tung Shan} and Hou, {Justin T.} and Hsu, {Te Wei}",
note = "Funding Information: The authors thank the referees for carefully reading the manuscript and providing helpful suggestions. The authors also thank Ting-Yuan Cheng for stimulating discussions. This research was partially supported by NSC grants 101-2115-M-390-004-MY3 (S.-P. Eu) and 101-2115-M-251-001 (T.-S. Fu).",
year = "2013",
month = sep,
doi = "10.1016/j.jcta.2013.06.007",
language = "English",
volume = "120",
pages = "1786--1803",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
number = "7",
}