I just came into contact with matroid theory through James Oxley's book 'Matroid Theory (2011)', and I was stuck on a problem while doing the exercises in the first section of Chapter 1:
Deduce that, as $n\rightarrow\infty$,the proportions of non-isomorphic $n$-element matroids that are graphic or are $GF(2)$-representable both tend to $0$.
I tried to find a lower bound for the number of n-isomorphic $n$-element matroids by recursive induction. I have also tried to list representable matroids over some fields with small sizes, I guess the proportion still tends to $0$ even if only placed in the representable matroids. But all fail. Any suggestions or literature for reference? Thank you~
