Tropical mixtures of star tree metrics
Algebraic Geometry
2011-09-06 v2 Combinatorics
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 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 taxa is unbounded.
Cite
@article{arxiv.0907.2053,
title = {Tropical mixtures of star tree metrics},
author = {Maria Angelica Cueto},
journal= {arXiv preprint arXiv:0907.2053},
year = {2011}
}
Comments
19 pages, 5 figures. Major revision of the exposition following suggestions by the referee. To appear in Annals of Combinatorics