Algebraic characteristic sets of matroids
For a matroid M, define the algebraic characteristic set \(\chi_ A(M)\) to be the set of field characteristics over which M can be algebraically represented. We construct many examples of rank three matroids with finite, non-singleton algebraic characteristic sets. We also determine \(\chi_ A(PG(2,p))\) and \(\chi_ A(AG(2,p))\). An infinite family of rank matroids with empty algebraic characteristic set is constructed. In addition, we answer some antichain and excluded minor questions for algebraic representability over a given field F.
scientific article; zbMATH DE number 3946152
scientific article