Enumeration of extensions of the cycle matroid of a complete graph

Peter Nelson, Shayla Redlin, Jorn van der Pol

We prove that the number of single element extensions of $M(K_{n+1})$ is $2^{\left(\genfrac{}{}{0ex}{}{n}{n/2}\right)(1+o(1))}$. This is done using a characterization of extensions as "linear subclasses".