P. Nelson

Unavoidable flats in GF(q)-representable matroids

We show that, for any finite field $\mathbb{F}$ and positive integer $k$, a simple $\mathbb{F}$-representable matroid $M$ with sufficiently high rank contains a rank-$k$ flat which is either independent in $M$, or is a projective or affine geometry over a subfield of $\mathbb{F}$. This generalizes a result for matroids...