The polytopal structure of the tight-span of a totally split-decomposable metric
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.
Keywords
Cite
@article{arxiv.1804.01821,
title = {The polytopal structure of the tight-span of a totally split-decomposable metric},
author = {K. T. Huber and J. Koolen and V. Moulton},
journal= {arXiv preprint arXiv:1804.01821},
year = {2018}
}