## 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.

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 language | English |
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Article number | 1701.06384v2 |

Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | arXiv |

Issue number | 1701.06384v2 |

Publication status | Published - 23 Jan 2017 |