A short proof of non-GF(5)-representability of matroids (Q1826956)

Rota conjectured that for any finite field \(F\) there are only finitely many minor-minimal non-\(F\)-representable matroids. This conjecture, if true, would provide a method for proving non-\(F\)-representability that requires a constant number of rank evaluations. Rota's conjecture is only known to be true for fields of size 2, 3 and 4. In this paper, the authors provide a method for proving non-GF(5)-representability that requires only \(O(n^2)\) rank evaluations, where \(n\) is the number of elements of the matroid.