The number of rank-$k$ flats in a matroid with no $U_{2,n}$-minor

Abstract

We show that, if $k$ and $\ell$ are positive integers and $r$ is sufficiently large, then the number of rank-$k$ flats in a rank-$r$ matroid $M$ with no $U_{2,\ell +2}$-minor is less than or equal to number of rank-$k$ flats in a rank-$r$ projective geometry over GF$(q)$, where $q$ is the largest prime power not exceeding $\ell$.

References in corpus (1)

• A Density Hales-Jewett Theorem for matroids

Cited by in corpus (1)

• The number of lines in a matroid with no $U_{2,n}$-minor