It was conjectured by White in 1980 that the toric ring associated to a matroid is defined symmetric exchange relations. This conjecture extended discrete polymatroids Herzog and Hibi, they prove holds for with so called strong property. In this paper we generalize their result are products of also extends Conca on transversal polymatroids.

The class of square matrices order n having a negative determinant and all their minors up to n−1 nonnegative is considered. A characterization these presented which provides an easy test based on the Cauchon algorithm for recognition. Furthermore, maximum allowable perturbation entry in position (2,2) such that perturbed matrix remains this given. Finally, it shown lying between two with respe...