An extension of Lindström's result about characteristic sets of matroids
If A is a (0,1)-matrix then \(M_ p(A)\) is the column space matroid of [I,A] over GF(p). Let \(\chi\) (M) and \(\chi_{alg}(M)\) denote the set of characteristics of the fields over which M is linearly (respectively algebraically) representable. The author proves ``under a fairly general hypothesis on A'' that \(\chi (M_ p(A))=\{q:\) \(M_ p(A)=M_ q(A)\}\) and \(\chi_{alg}(M_ p(A))\subseteq \{q:\) \(M_ p(A)\geq M_ q(A)\}\) where \(M\geq N\) means that every circuit of M contains a circuit of N.
scientific article; zbMATH DE number 4023305