Algebraic matroids and Frobenius flocks

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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 {\em Lindstr\"om 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 Lindstr\"om valuation, we introduce new matroid representations called flocks, and show that each algebraic representation of a matroid induces flock representations.
Original languageEnglish
Article number1701.06384v2
Pages (from-to)1-21
Number of pages21
JournalarXiv
Issue number1701.06384v2
Publication statusPublished - 23 Jan 2017

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