Pfaffian forms and \(\Delta\)-matroids (Q1801704)

It is proved that skew-symmetric \(n \times n\) matrices with coefficients in a field \({\mathfrak K}\) correspond via Pfaffian forms in a canonical one- to-one fashion to \({\mathfrak K}\)-value maps defined on the power set \({\mathfrak P} (\{1, \dots, n\})\), which satisfy certain identities in Section 2. The representability of \(\Delta\)-matroids by skew-symmetric matrices in terms of Pfaffian maps is described as an application in Section 3.