Standard Young Tableaux and Colored Motzkin Paths

Standard Young Tableaux and Colored Motzkin Paths

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 rev...

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Hauptverfasser: Eu, Sen-Peng, Fu, Tung-Shan, Hou, Justin T, Hsu, Te-Wei
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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Zusammenfassung: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.
DOI:10.48550/arxiv.1302.3012