Combinatorial invariants of finite metric spaces and the Wasserstein arrangement
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909608114651136 |
|---|---|
| author | Delucchi, Emanuele Kühne, Lukas Mühlherr, Leonie |
| author_facet | Delucchi, Emanuele Kühne, Lukas Mühlherr, Leonie |
| contents | In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport and are called ``Wasserstein polytopes'' or ``Kantorovich-Rubinstein polytopes'' in the literature. Answering a question posed by Vershik, we describe the stratification of the metric cone induced by the combinatorial type of these polytopes through a hyperplane arrangement. Moreover, we study its relationships with the stratification by combinatorial type of the injective hull (i.e., the tight span) and, in particular, with certain types of metrics arising in phylogenetic analysis. We also compute enumerative invariants in the case of metrics on up to six points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial invariants of finite metric spaces and the Wasserstein arrangement Delucchi, Emanuele Kühne, Lukas Mühlherr, Leonie Combinatorics In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport and are called ``Wasserstein polytopes'' or ``Kantorovich-Rubinstein polytopes'' in the literature. Answering a question posed by Vershik, we describe the stratification of the metric cone induced by the combinatorial type of these polytopes through a hyperplane arrangement. Moreover, we study its relationships with the stratification by combinatorial type of the injective hull (i.e., the tight span) and, in particular, with certain types of metrics arising in phylogenetic analysis. We also compute enumerative invariants in the case of metrics on up to six points. |
| title | Combinatorial invariants of finite metric spaces and the Wasserstein arrangement |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.15584 |