Flats and hyperplane arrangements for matroids with coefficients
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908876394201088 |
|---|---|
| author | Koulman, Jannis Lorscheid, Oliver |
| author_facet | Koulman, Jannis Lorscheid, Oliver |
| contents | Based on the notion of vectors and linear subspaces for a matroid, we develop a theory of flats and hyperplane arrangements for T-matroids, where T is a tract. This leads to several cryptomorphic descriptions of T-matroids: in terms of its lattice of T-flats, as a hyperplane arrangement over T, as point-line arrangements in projective space over T and as a quiver representation over T. We examplify these notions in the case of tropical linear spaces, a.k.a. valuated matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09516 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flats and hyperplane arrangements for matroids with coefficients Koulman, Jannis Lorscheid, Oliver Combinatorics Based on the notion of vectors and linear subspaces for a matroid, we develop a theory of flats and hyperplane arrangements for T-matroids, where T is a tract. This leads to several cryptomorphic descriptions of T-matroids: in terms of its lattice of T-flats, as a hyperplane arrangement over T, as point-line arrangements in projective space over T and as a quiver representation over T. We examplify these notions in the case of tropical linear spaces, a.k.a. valuated matroids. |
| title | Flats and hyperplane arrangements for matroids with coefficients |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.09516 |