Pfaffian forms and Δ-matroids with coefficients

Walter Wenzel
1996 Discrete Mathematics  
In this paper I begin to build up a theory of A-matroids with coefficients parallel to the theory of matroids with coefficients. While the definition of a matroid with coefficients is based on the well-known Grassmann identity concerning determinants, a quite similar identity concerning Pfaffian forms leads to the theory of A-matroids with coefficients. Particular examples are A-matroids representable by some skew-symmetric matrix with coefficients in a field, oriented A-matroids, and valuated A-matroids.
doi:10.1016/0012-365x(94)00172-f fatcat:4oz2hpquljc7bgq7tcwa2op2gu