On the complex-representable excluded minors for real-representability

Abstract

We show that each real-representable matroid is a minor of a complex-representable excluded minor for real-representability. More generally, for an infinite field ${\mathbb{F}}_1$ and a field extension ${\mathbb{F}}_2$, if ${\mathbb{F}}_1$-representability is not equivalent to ${\mathbb{F}}_2$-representability, then each ${\mathbb{F}}_1$-representable matroid is a minor of a ${\mathbb{F}}_2$-representable excluded minor for ${\mathbb{F}}_1$-representability.

14 pages, 2 figures. Submitted for publication in JCTb