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arXiv · 1804.01821

The polytopal structure of the tight-span of a totally split-decomposable metric

K. T. Huber·J. Koolen·V. Moulton
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Abstract

The tight-span of a finite metric space is a polytopal complex that has appeared in several areas of mathematics. In this paper we determine the polytopal structure of the tight-span of a totally split decomposable (finite) metric. Totally split-decomposable metrics are a generalization of tree-metrics and have importance within phylogenetics. In previous work, we showed that the cells of the tight-span of such a metric are zonotopes that are polytope isomorphic to either hypercubes or rhombic dodecahedra. Here, we extend these results and show that the tight-spanof a totally split-decomposable metric can be broken up into a canonical collection of polytopal complexes whose polytopal structures can be directly determined from the metric. This allows us to also completely determine the polytopal structure of the tight-span of a totally split-decomposable metric in a very direct way.We anticipate that our improved understanding of this structure may ultimately lead to improved techniques for phylogenetic inference.

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K. T. Huber, J. Koolen, V. Moulton. 2018-04-05. The polytopal structure of the tight-span of a totally split-decomposable metric. https://arxiv.org/abs/1804.01821

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