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
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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
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 328533
- DOI 10.1016/j.ejc.2020.103098
- Persistent URL
- https://folia.unifr.ch/unifr/documents/308717
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