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Standard Young tableaux and colored Motzkin paths |
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| Authors: | Sen-Peng Eu Tung-Shan Fu Justin T. Hou Te-Wei Hsu |
| Affiliation: | 1. Department of Applied Mathematics, National University of Kaohsiung, and Chinese Air Force Academy, Kaohsiung 811, Taiwan, ROC;2. Mathematics Faculty, National Pingtung Institute of Commerce, Pingtung 900, Taiwan, ROC;3. Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan, ROC;4. Department of Physics, National Taiwan University, Taipei 106, Taiwan, ROC |
| 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 rows and the set of SYTs with at most 2d rows. |
| Keywords: | Standard Young tableaux Colored Motzkin paths Shuffles of parenthesis systems Bijection |
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