The polytope of all matroids in ranks 2 and 3
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909037820379136 |
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| author | Collins, Narayan Schleis, Victoria |
| author_facet | Collins, Narayan Schleis, Victoria |
| contents | We give explicit recursive constructions for the polytope of all matroids $Ω_{r,n}$ in ranks 2 and 3 for all ground set sizes. This polytope was introduced in recent work by Ferroni and Fink as a tool for checking positivity conjectures for valuative invariants. We supplement our theoretical construction by an implementation, which allows for the computation of $Ω_{2,n}$ for $n\leq 33$ and $Ω_{3,n}$ for $n\leq 10$. Further, we compute Schubert expansions for all isomorphism classes of matroids of rank $2$ up to $n = 80$, and for rank $3$ up to $n = 11$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12336 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The polytope of all matroids in ranks 2 and 3 Collins, Narayan Schleis, Victoria Combinatorics 05B35 (Primary), 52B40 (Secondary) We give explicit recursive constructions for the polytope of all matroids $Ω_{r,n}$ in ranks 2 and 3 for all ground set sizes. This polytope was introduced in recent work by Ferroni and Fink as a tool for checking positivity conjectures for valuative invariants. We supplement our theoretical construction by an implementation, which allows for the computation of $Ω_{2,n}$ for $n\leq 33$ and $Ω_{3,n}$ for $n\leq 10$. Further, we compute Schubert expansions for all isomorphism classes of matroids of rank $2$ up to $n = 80$, and for rank $3$ up to $n = 11$. |
| title | The polytope of all matroids in ranks 2 and 3 |
| topic | Combinatorics 05B35 (Primary), 52B40 (Secondary) |
| url | https://arxiv.org/abs/2605.12336 |