Enumeration of rooted binary perfect phylogenies
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916445759209472 |
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| author | Shiff, Chloe E. Rosenberg, Noah A. |
| author_facet | Shiff, Chloe E. Rosenberg, Noah A. |
| contents | Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable lineages associated with the leaf. For the rooted binary unlabeled trees, these integers equal 1. We address a variety of enumerative problems concerning rooted binary perfect phylogenies with sample size $s$: the rooted binary unlabeled trees in which a sample of size $s$ lineages is distributed across the leaves of an unlabeled tree with $n$ leaves, $1 \leq n \leq s$. The enumerations further characterize the rooted binary perfect phylogenies, which include the rooted binary unlabeled trees, and which can provide a set of structures useful for various biological contexts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_14915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumeration of rooted binary perfect phylogenies Shiff, Chloe E. Rosenberg, Noah A. Populations and Evolution Combinatorics 05A15, 05A16, 05C05, 92D15 Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable lineages associated with the leaf. For the rooted binary unlabeled trees, these integers equal 1. We address a variety of enumerative problems concerning rooted binary perfect phylogenies with sample size $s$: the rooted binary unlabeled trees in which a sample of size $s$ lineages is distributed across the leaves of an unlabeled tree with $n$ leaves, $1 \leq n \leq s$. The enumerations further characterize the rooted binary perfect phylogenies, which include the rooted binary unlabeled trees, and which can provide a set of structures useful for various biological contexts. |
| title | Enumeration of rooted binary perfect phylogenies |
| topic | Populations and Evolution Combinatorics 05A15, 05A16, 05C05, 92D15 |
| url | https://arxiv.org/abs/2410.14915 |