Enumerating runs, valleys, and peaks in Catalan words
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866929305991249920 |
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| author | Baril, Jean-Luc Harris, Pamela E. Harry, Kimberly J. McClinton, Matt Ramírez, José L. |
| author_facet | Baril, Jean-Luc Harris, Pamela E. Harry, Kimberly J. McClinton, Matt Ramírez, José L. |
| contents | We provide generating functions, formulas, and asymptotic expressions for the number of Catalan words based on the number of runs of ascents (descents), runs of weak ascents (descents), $\ell$-valleys, valleys, symmetric valleys, $\ell$-peaks, peaks, and symmetric peaks. We also establish some bijections with restricted Dyck paths and ordered trees that transports some statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumerating runs, valleys, and peaks in Catalan words Baril, Jean-Luc Harris, Pamela E. Harry, Kimberly J. McClinton, Matt Ramírez, José L. Combinatorics 05A15, 05A19 We provide generating functions, formulas, and asymptotic expressions for the number of Catalan words based on the number of runs of ascents (descents), runs of weak ascents (descents), $\ell$-valleys, valleys, symmetric valleys, $\ell$-peaks, peaks, and symmetric peaks. We also establish some bijections with restricted Dyck paths and ordered trees that transports some statistics. |
| title | Enumerating runs, valleys, and peaks in Catalan words |
| topic | Combinatorics 05A15, 05A19 |
| url | https://arxiv.org/abs/2404.05672 |