Algebraic matroids and Frobenius flocks

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Uittreksel

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.

TaalEngels
Pagina's688-719
Aantal pagina's32
TijdschriftAdvances in Mathematics
Volume323
DOI's
StatusGepubliceerd - 7 jan 2018

Vingerafdruk

Flock
Frobenius
Matroid
Valuation
Positive Characteristic
Trivial
Linear Representation
If and only if

Trefwoorden

    Citeer dit

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    title = "Algebraic matroids and Frobenius flocks",
    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 Lindstr{\"o}m 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{\"o}m valuation, we introduce new matroid representations called flocks, and show that each algebraic representation of a matroid induces flock representations.",
    keywords = "Algebraic matroids, Matroid valuations",
    author = "G.P. Bollen and J. Draisma and R. Pendavingh",
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    doi = "10.1016/j.aim.2017.11.006",
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    Algebraic matroids and Frobenius flocks. / Bollen, G.P.; Draisma, J.; Pendavingh, R.

    In: Advances in Mathematics, Vol. 323, 07.01.2018, blz. 688-719.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    TY - JOUR

    T1 - Algebraic matroids and Frobenius flocks

    AU - Bollen,G.P.

    AU - Draisma,J.

    AU - Pendavingh,R.

    PY - 2018/1/7

    Y1 - 2018/1/7

    N2 - 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.

    AB - 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.

    KW - Algebraic matroids

    KW - Matroid valuations

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    U2 - 10.1016/j.aim.2017.11.006

    DO - 10.1016/j.aim.2017.11.006

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