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Tropical Mixtures of Star Tree Metrics

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Abstract

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 weights satisfy 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 fixed taxa is unbounded.

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Authors and Affiliations

  1. Mathematics Department, Columbia University, MC 4403, 2990 Broadway, New York, NY, 10027, USA

    María Angélica Cueto

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  1. María Angélica Cueto
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Correspondence to María Angélica Cueto.

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The author was supported by a UC Berkeley Chancellor’s Fellowship and the Laboratory for Mathematical and Computational Biology at UC Berkeley.

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Cueto, M.A. Tropical Mixtures of Star Tree Metrics. Ann. Comb. 16, 233–251 (2012). https://doi.org/10.1007/s00026-012-0128-7

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  • DOI: https://doi.org/10.1007/s00026-012-0128-7

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