Fundamental polytopes of metric trees via parallel connections of matroids

Delucchi, Emanuele and Hoessly, Linard (2020) Fundamental polytopes of metric trees via parallel connections of matroids. European Journal of Combinatorics, 87. p. 103098. ISSN 01956698

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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 (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. • We characterize the metric trees for which the fundamental polytope is simplicial.

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