Standard Young tableaux and colored Motzkin paths

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

doi:10.1016/j.jcta.2013.06.007

Standard Young tableaux and colored Motzkin paths

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1786-1803
Number of pages	18
Journal	Journal of Combinatorial Theory. Series A
Volume	120
Issue number	7
DOIs	https://doi.org/10.1016/j.jcta.2013.06.007
Publication status	Published - 2013 Sept
Externally published	Yes

Keywords

Bijection
Colored Motzkin paths
Shuffles of parenthesis systems
Standard Young tableaux

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2013.06.007

Cite this

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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",

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TY - JOUR

T1 - Standard Young tableaux and colored Motzkin paths

AU - Eu, Sen Peng

AU - Fu, Tung Shan

AU - Hou, Justin T.

AU - Hsu, Te Wei

N1 - 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).

PY - 2013/9

Y1 - 2013/9

N2 - 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.

AB - 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.

KW - Bijection

KW - Colored Motzkin paths

KW - Shuffles of parenthesis systems

KW - Standard Young tableaux

UR - https://www.scopus.com/pages/publications/84880164893

UR - https://www.scopus.com/pages/publications/84880164893#tab=citedBy

U2 - 10.1016/j.jcta.2013.06.007

DO - 10.1016/j.jcta.2013.06.007

M3 - Article

AN - SCOPUS:84880164893

SN - 0097-3165

VL - 120

SP - 1786

EP - 1803

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 7

ER -

Standard Young tableaux and colored Motzkin paths

Abstract

Keywords

ASJC Scopus subject areas

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