On some combinatorial properties of algebraic matroids
The minimax theorem for matroid matching, originally proved for linear matroids only [\textit{L. Lovász}, Acta Sci. Math. 42, 121-131 (1980; Zbl 0449.51008)] is shown to hold for algebraic matroids as well. The main tool of the proof is a generalization of a lemma (implicitly proved by Ingleton and Main, explicitly by Lindström) that if three lines in the algebraic matroid consisting all elements of an algebraically closed field are not coplanar but any two of them are then they pass through one point.
scientific article; zbMATH DE number 4019083
scientific article