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Enumerating Matroids and Linear Spaces
- Source :
- Comptes Rendus. Mathématique, Vol 361, Iss G2, Pp 565-575 (2023)
- Publication Year :
- 2023
- Publisher :
- Académie des sciences, 2023.
-
Abstract
- 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 $n$.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English, French
- ISSN :
- 17783569
- Volume :
- 361
- Issue :
- G2
- Database :
- Directory of Open Access Journals
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.167138ee6c0a42da98a433d2544332d4
- Document Type :
- article
- Full Text :
- https://doi.org/10.5802/crmath.423