On some combinatorial properties of algebraic matroids

Abstract

It was proved implicitly by Ingleton and Main and explicitly by Lindström that if three lines in the algebraic matroid consisting of all elements of an algebraically closed field are not coplanar, but any two of them are, then they pass through one point. This theorem is extended to a more general result about the intersection of subspaces in full algebraic matroids. This result is used to show that the minimax theorem for matroid matching, proved for linear matroids by Lovász, remains valid for algebraic matroids.

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Dress, A., Lovász, L. On some combinatorial properties of algebraic matroids. Combinatorica 7, 39–48 (1987). https://doi.org/10.1007/BF02579199

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AMS subject classification (1980)

  • 05 B 35