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

UR - http://www.scopus.com/inward/record.url?scp=85033698486&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2017.11.006

DO - 10.1016/j.aim.2017.11.006

M3 - Article

AN - SCOPUS:85033698486

SN - 0001-8708

VL - 323

SP - 688

EP - 719

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -