# 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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