Enumerating Matroids of Fixed Rank

@article{Pendavingh2015EnumeratingMO,
  title={Enumerating Matroids of Fixed Rank},
  author={Rudi Pendavingh and Jorn G. van der Pol},
  journal={Electron. J. Comb.},
  year={2015},
  volume={24},
  pages={1}
}
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that $s(n) \sim m(n)$, where $m(n)$ denotes the number of matroids on a fixed groundset of size $n$, and $s(n)$ the number of sparse paving matroids. In an earlier paper, we showed that $\log s(n) \sim \log m(n)$. The bounds that we used for that result were dominated by matroids of rank $r\approx n/2$. In this paper we consider the relation between the number of sparse paving matroids $s(n,r)$ and the… 

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