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arXiv · 1612.05534

Fundamental polytopes of metric trees via parallel connections of matroids

Emanuele Delucchi·Linard Hoessly
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Abstract

We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.

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Emanuele Delucchi, Linard Hoessly. 2019-04-01. Fundamental polytopes of metric trees via parallel connections of matroids. https://doi.org/10.1016/j.ejc.2020.103098

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