Tropical mixtures of star tree metrics
| Autor: | Maria Angelica Cueto |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Tree rotation
Discrete mathematics K-ary tree Star (graph theory) Interval tree Combinatorics Set (abstract data type) 52B70 15A03 14M25 Mathematics - Algebraic Geometry Tree (data structure) Metric (mathematics) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Algebraic Geometry (math.AG) Vantage-point tree Mathematics |
| DOI: | 10.48550/arxiv.0907.2053 |
| Popis: | We study tree metrics that can be realized as a mixture of two star tree metrics. We prove that the only trees admitting such a decomposition are the ones coming from a tree with at most one internal edge, and whose weight satisfies certain linear inequalities. We also characterize the fibers of the corresponding mixture map. In addition, we discuss the general framework of tropical secant varieties and we interpret our results within this setting. Finally, we show that the set of tree metric ranks of metrics on $n$ taxa is unbounded. Comment: 19 pages, 5 figures. Major revision of the exposition following suggestions by the referee. To appear in Annals of Combinatorics |
| Databáze: | OpenAIRE |
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