Algebraic matroids and Frobenius flocks

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
54 Downloads (Pure)

Abstract

We show that each algebraic representation of a matroid M in positive characteristic determines a matroid valuation of M, which we have named the Lindström valuation. If this valuation is trivial, then a linear representation of M in characteristic p can be derived from the algebraic representation. Thus, so-called rigid matroids, which only admit trivial valuations, are algebraic in positive characteristic p if and only if they are linear in characteristic p. To construct the Lindström valuation, we introduce new matroid representations called flocks, and show that each algebraic representation of a matroid induces flock representations.

Original languageEnglish
Pages (from-to)688-719
Number of pages32
JournalAdvances in Mathematics
Volume323
DOIs
Publication statusPublished - 7 Jan 2018

    Fingerprint

Keywords

  • Algebraic matroids
  • Matroid valuations

Cite this