Geodesic
Combinatoire
Enumerating Matroids and Linear Spaces
Kwan, Matthew1 ; Sah, Ashwin2 ; Sawhney, Mehtaab2 
1 Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Comptes Rendus. Mathématique, Tome 361 (2023) no. G2, pp. 565-575

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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 3/2-3 (1+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≥4 there are (e 1-r n+o(n)) n r-1 /r! rank-r matroids on a ground set of size n.

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DOI : 10.5802/crmath.423

Kwan, Matthew 1 ; Sah, Ashwin 2 ; Sawhney, Mehtaab 2

1 Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Enumerating {Matroids} and {Linear} {Spaces}},
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Kwan, Matthew; Sah, Ashwin; Sawhney, Mehtaab. Enumerating Matroids and Linear Spaces. Comptes Rendus. Mathématique, Tome 361 (2023) no. G2, pp. 565-575. doi: 10.5802/crmath.423

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