| Autor: |
Kwan, Matthew, Sah, Ashwin, Sawhney, Mehtaab |
| Jazyk: |
English<br />French |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Comptes Rendus. Mathématique, Vol 361, Iss G2, Pp 565-575 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
1778-3569 |
| DOI: |
10.5802/crmath.423 |
| Popis: |
We show that the number of linear spaces on a set of $n$ points and the number of rank-3 matroids on a ground set of size $n$ are both of the form $(cn+o(n))^{n^2/6}$, where $c=e^{\sqrt{3}/2-3}(1+\sqrt{3})/2$. This is the final piece of the puzzle for enumerating fixed-rank matroids at this level of accuracy: there are exact formulas for enumeration of rank-1 and rank-2 matroids, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant $r\ge 4$ there are $(e^{1-r}n+o(n))^{n^{r-1}/r!}$ rank-$r$ matroids on a ground set of size $n$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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