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Mathematics > Combinatorics

arXiv:1812.08692 (math)
[Submitted on 20 Dec 2018 (v1), last revised 18 Mar 2020 (this version, v2)]

Title:Matroids over one-dimensional groups

Authors:Guus P. Bollen, Dustin Cartwright, Jan Draisma
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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.
Comments: 29 pages, 4 diagrams, 2 pictures, improved exposition---many thanks to referees!
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG); Rings and Algebras (math.RA)
Cite as: arXiv:1812.08692 [math.CO]
  (or arXiv:1812.08692v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1812.08692
Journal reference: Int. Math. Res. Not., 2022:3, 2298-2336
Related DOI: https://doi.org/10.1093/imrn/rnaa175

Submission history

From: Jan Draisma [view email]
[v1] Thu, 20 Dec 2018 16:51:45 UTC (183 KB)
[v2] Wed, 18 Mar 2020 14:14:17 UTC (186 KB)
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