Some statistics in Dyck paths, non-crossing partitions, and 2-Motzkin paths
碩士 === 國立高雄大學 === 應用數學系碩士班 === 103 === In this study, we use two bijections: one is between non-crossing partitions and Dyck paths, and the other is between 2-Motzkin paths and Dyck paths. We obtain the generating function of statistics edes, odes, easc, and oasc in Dyck paths. Moreover, we derive t...
| Main Authors: | , |
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| Format: | Others |
| Language: | en_US |
| Published: |
2015
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| Online Access: | http://ndltd.ncl.edu.tw/handle/05274681290044074372 |
| Summary: | 碩士 === 國立高雄大學 === 應用數學系碩士班 === 103 === In this study, we use two bijections: one is between non-crossing partitions and Dyck paths, and the other is between 2-Motzkin paths and Dyck paths. We obtain the generating function of statistics edes, odes, easc, and oasc in Dyck paths. Moreover, we derive the enumerating polynomials of the statistics emaj, omaj, ecomaj, and ocomaj in Dyck paths. The corresponding results for non-crossing partitions, and 2-Motzkin paths are also discussed.
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