Matroids over one-dimensional groups
Combinatorics
2023-01-10 v2 Algebraic Geometry
Rings and Algebras
Abstract
We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindstr\"om 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 Lindstr\"om valuations, is not closed under duality of valuated matroids.
Keywords
Cite
@article{arxiv.1812.08692,
title = {Matroids over one-dimensional groups},
author = {Guus P. Bollen and Dustin Cartwright and Jan Draisma},
journal= {arXiv preprint arXiv:1812.08692},
year = {2023}
}
Comments
29 pages, 4 diagrams, 2 pictures, improved exposition---many thanks to referees!