Turán densities for matroid basis hypergraphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910866574671872 |
|---|---|
| author | van der Pol, Jorn Walsh, Zach Wigal, Michael C. |
| author_facet | van der Pol, Jorn Walsh, Zach Wigal, Michael C. |
| contents | Let $U$ be a uniform matroid. For all positive integers $n$ and $r$ with $n \ge r$, what is the maximum number of bases of an $n$-element, rank-$r$ matroid without $U$ as a minor? We show that this question arises by restricting the problem of determining the Turán number of a daisy hypergraph to the family of matroid basis hypergraphs. We then answer this question for several interesting choices of $U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Turán densities for matroid basis hypergraphs van der Pol, Jorn Walsh, Zach Wigal, Michael C. Combinatorics Let $U$ be a uniform matroid. For all positive integers $n$ and $r$ with $n \ge r$, what is the maximum number of bases of an $n$-element, rank-$r$ matroid without $U$ as a minor? We show that this question arises by restricting the problem of determining the Turán number of a daisy hypergraph to the family of matroid basis hypergraphs. We then answer this question for several interesting choices of $U$. |
| title | Turán densities for matroid basis hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.03673 |