A note on plane trees with decreasing labels
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908860670803968 |
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| author | Cheung, Tsun-Ming Devroye, Luc Goh, Marcel K. |
| author_facet | Cheung, Tsun-Ming Devroye, Luc Goh, Marcel K. |
| contents | This note derives asymptotic upper and lower bounds for the number of planted plane trees on $n$ nodes assigned labels from the set $\{1,2,\ldots, k\}$ with the restriction that on any path from the root to a leaf, the labels must strictly decrease. We illustrate an application to calculating the largest eigenvalue of the adjacency matrix of a tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on plane trees with decreasing labels Cheung, Tsun-Ming Devroye, Luc Goh, Marcel K. Combinatorics 05C05, 05C30, 05C50 This note derives asymptotic upper and lower bounds for the number of planted plane trees on $n$ nodes assigned labels from the set $\{1,2,\ldots, k\}$ with the restriction that on any path from the root to a leaf, the labels must strictly decrease. We illustrate an application to calculating the largest eigenvalue of the adjacency matrix of a tree. |
| title | A note on plane trees with decreasing labels |
| topic | Combinatorics 05C05, 05C30, 05C50 |
| url | https://arxiv.org/abs/2502.14596 |