Matroids Over One-Dimensional Groups-Reference-Cited by-同舟云学术

Matroids Over One-Dimensional Groups

Published:2020-07-24 Issue:3 Volume:2022 Page:2298-2336
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bollen Guus P¹,Cartwright Dustin²,Draisma Jan³

Affiliation:

1. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

2. Department of Mathematics, University of Tennessee, 227 Ayres Hall, Knoxville, TN 37996-1320, USA

3. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland; and Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Abstract

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.

Funder

NWO Vici

Stichting Computer Algebra Nederland

NSA Young Investigator

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2022/3/2298/42324971/rnaa175.pdf

Reference26 articles.

1. Matroids over partial hyperstructures;Baker;Adv. Math.,2019

2. Algebraic matroids and Frobenius flocks;Bollen;Adv. Math.,2018

3. Linear Algebraic Groups

4. Construction of the Lindström valuation of an algebraic extension;Cartwright;J. Comb. Theory, Ser. A,2018