Fundamental polytopes of metric trees via parallel connections of matroids

Delucchi, Emanuele; Hoessly, Linard

doi:10.1016/j.ejc.2020.103098

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Journal article

Fundamental polytopes of metric trees via parallel connections of matroids

Delucchi, Emanuele Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700, Fribourg, Switzerland
Hoessly, Linard Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700, Fribourg, Switzerland

25.03.2020

Published in:

European Journal of Combinatorics. - 2020, vol. 87, p. 103098

English 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.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language