Enumeration of multipartite series-reduced trees
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914209620557824 |
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| author | Jumadildayev, Medet |
| author_facet | Jumadildayev, Medet |
| contents | We obtain a generating function for the degree sequences and colors of rooted multipartite labeled series-reduced trees. As an application of this result, we determine the number of symbolic ultrametrics (introduced by Böcker and Dress) and increasingly labeled processes. We also find that the number of multipartite labeled series-reduced trees and the colored chain-increasing binary trees are the same. We obtain the number of rooted multipartite unlabeled series-reduced trees. We also find a refinement of the result of Riordan and Shannon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of multipartite series-reduced trees Jumadildayev, Medet Combinatorics 05C05, 05C07, 05C15, 11B73 We obtain a generating function for the degree sequences and colors of rooted multipartite labeled series-reduced trees. As an application of this result, we determine the number of symbolic ultrametrics (introduced by Böcker and Dress) and increasingly labeled processes. We also find that the number of multipartite labeled series-reduced trees and the colored chain-increasing binary trees are the same. We obtain the number of rooted multipartite unlabeled series-reduced trees. We also find a refinement of the result of Riordan and Shannon. |
| title | Enumeration of multipartite series-reduced trees |
| topic | Combinatorics 05C05, 05C07, 05C15, 11B73 |
| url | https://arxiv.org/abs/2512.17216 |