Matroid polytopes with small rank
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908288641138688 |
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| author | Konoike, Masato Matsushita, Koji |
| author_facet | Konoike, Masato Matsushita, Koji |
| contents | For a lattice polytope $P$, the rank of $P$ is defined by $F-(\dim P+1)$, where $F$ is the number of facets of $P$. In this paper, we study matroid polytopes with small rank. More precisely, we characterize matroid independence polytopes and graphic matroid base polytopes with rank at most three. Furthermore, using this characterization, we investigate their relationships with order polytopes, stable set polytopes, and edge polytopes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_22514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matroid polytopes with small rank Konoike, Masato Matsushita, Koji Combinatorics Primary: 52B20, Secondary: 05B35, 52B40 For a lattice polytope $P$, the rank of $P$ is defined by $F-(\dim P+1)$, where $F$ is the number of facets of $P$. In this paper, we study matroid polytopes with small rank. More precisely, we characterize matroid independence polytopes and graphic matroid base polytopes with rank at most three. Furthermore, using this characterization, we investigate their relationships with order polytopes, stable set polytopes, and edge polytopes. |
| title | Matroid polytopes with small rank |
| topic | Combinatorics Primary: 52B20, Secondary: 05B35, 52B40 |
| url | https://arxiv.org/abs/2503.22514 |