Algebraic matroids and Frobenius flocks

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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
Publication statusPublished - 7 Jan 2018


  • Algebraic matroids
  • Matroid valuations


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