On the complex-representable excluded minors for real-representability

2018/01/26 by Campbell, Rutger, Geelen, Jim
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08656

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 \mathbbF₁ and a field extension \mathbbF₂, if \mathbbF₁-representability is not equivalent to \mathbbF₂-representability, then each \mathbbF₁-representable matroid is a minor of a \mathbbF₂-representable excluded minor for \mathbbF₁-representability.

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