# Paving matroid

A matroid M is called paving if every set of size r(M)-1 is independent. It is called sparse paving if in addition every circuit of size r(M) is closed. The importance of (sparse) paving matroids stems from their large number: lower bounds on the number of matroids are obtained by counting sparse paving matroids, see e.g. Knuth [1]. In fact, Mayhew et al. [2] conjecture that if $m_n$ is the number of matroids and $s_n$ is the number of sparse paving matroids on $n$ elements, then $\lim_{n \to \infty} \frac{m_n}{s_n} =1$. Progress towards this conjecture has been made in [3].