Doubly Exponentially Many Ingleton Matroids
Peter Nelson, Jorn van der Pol · SIAM Journal on Discrete Mathematics · 2018
A matroid is Ingleton if all quadruples of subsets of its ground set satisfy Ingleton's inequality. In particular, representable matroids are Ingleton. We show that the number of Ingleton matroids on ground set $[n]$ is doubly exponential in $n$; it follows that almost all Ingleton matroids are nonrepresentable.