Representability of \(\bigtriangleup\)-matroids over \(GF(2)\) (Q1174313)

A \(\Delta\)-matroid is a set system \(S=(V,F)\) where the elements of \(F\) are subsets of \(V\) and satisfy that for every \(F'\), \(F''\in F\), \(x\in F'\Delta F''\), there exists \(y\in F'\Delta F''\) so that \(F'\Delta\{x,y\}\in F\). (Here \(\Delta\) denotes symmetric difference.) The collection of the nonsingular symmetric minors of a symmetric binary matrix satisfies this property. The authors characterize those \(\Delta\)- matroids which arise in this way, generalizing Tutte's theorem for binary matroids, and present further results on strong and weak representability of \(\Delta\)-matroids over \(GF(2)\).