Maximally probable tree topologies with $r$-furcation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915784086781952 |
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| author | Dickey, Emily H. Rosenberg, Noah A. |
| author_facet | Dickey, Emily H. Rosenberg, Noah A. |
| contents | For a specific rooted labeled tree topology, a labeled history is a sequence of branchings that give rise to that labeled topology as it unfolds over time. Here, for $r$-furcating trees, we use a connection with Huffman trees from information theory to identify maximally probable rooted trees -- unlabeled $r$-furcating topologies whose labelings each have a number of labeled histories greater than or equal to those of all other labeled topologies. Our characterization of the unique maximally probable $r$-furcating unlabeled topology generalizes the Harding--Hammersley--Grimmett result identifying the maximally probable bifurcating unlabeled topology, and it provides a new proof for that result. We present a conjecture for the maximally probable $r$-furcating unlabeled topology if labeled histories are tabulated allowing for simultaneous branching events across multiple internal nodes of a tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximally probable tree topologies with $r$-furcation Dickey, Emily H. Rosenberg, Noah A. Combinatorics Populations and Evolution 60C05, 05C05, 92D15, 94A45 For a specific rooted labeled tree topology, a labeled history is a sequence of branchings that give rise to that labeled topology as it unfolds over time. Here, for $r$-furcating trees, we use a connection with Huffman trees from information theory to identify maximally probable rooted trees -- unlabeled $r$-furcating topologies whose labelings each have a number of labeled histories greater than or equal to those of all other labeled topologies. Our characterization of the unique maximally probable $r$-furcating unlabeled topology generalizes the Harding--Hammersley--Grimmett result identifying the maximally probable bifurcating unlabeled topology, and it provides a new proof for that result. We present a conjecture for the maximally probable $r$-furcating unlabeled topology if labeled histories are tabulated allowing for simultaneous branching events across multiple internal nodes of a tree. |
| title | Maximally probable tree topologies with $r$-furcation |
| topic | Combinatorics Populations and Evolution 60C05, 05C05, 92D15, 94A45 |
| url | https://arxiv.org/abs/2602.07426 |