@article{15173,
  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))n2/6, where c=e3√/2−3(1+3–√)/2. This is the final piece of the puzzle for enumerating fixed-rank matroids at this level of accuracy: the numbers of rank-1 and rank-2 matroids on a ground set of size n have exact representations in terms of well-known combinatorial functions, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant r≥4 there are (e1−rn+o(n))nr−1/r! rank-r matroids on a ground set of size n. In our proof, we introduce a new approach for bounding the number of clique decompositions of a complete graph, using quasirandomness instead of the so-called entropy method that is common in this area.},
  author       = {Kwan, Matthew Alan and Sah, Ashwin and Sawhney, Mehtaab},
  issn         = {1778-3569},
  journal      = {Comptes Rendus Mathematique},
  number       = {G2},
  pages        = {565--575},
  publisher    = {Academie des Sciences},
  title        = {{Enumerating matroids and linear spaces}},
  doi          = {10.5802/crmath.423},
  volume       = {361},
  year         = {2023},
}