Matroids over one-dimensional groups

Abstract

We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindström valuations and Frobenius flocks of such matroids. Building on work by Evans and Hrushovski, we show that the class of algebraic matroids, paired with their Lindström valuations, is not closed under duality of valuated matroids.

29 pages, 4 diagrams, 2 pictures, improved exposition---many thanks to referees!

References in corpus (2)

• Field extensions, Derivations, and Matroids over Skew Hyperfields
• Stanley-Reisner rings for symmetric simplicial complexes, G-semimatroids and Abelian arrangements

Cited by in corpus (1)

• Common Information, Matroid Representation, and Secret Sharing for Matroid Ports