Algebraic matroids and Frobenius flocks

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Samenvatting

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.
Originele taal-2Engels
Artikelnummer1701.06384v2
Pagina's (van-tot)1-21
Aantal pagina's21
TijdschriftarXiv
Nummer van het tijdschrift1701.06384v2
StatusGepubliceerd - 23 jan 2017

Bibliografische nota

21 pages, 1 figure

Trefwoorden

  • math.CO
  • math.AG
  • 05E40 Combinatorial aspects of commutative algebra, 05B35 Matroids, geometric lattices

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