The Alpha Function of a Matroid—I. Transversal Matroids

摘要

Letnbe the nullity function of the matroidG(S). The Mason alpha function is defined on subsetsAofSby the recursion α(A)=n(A)−∑F⊂Aα(F), the summation being over all flatsFstrictly contained inA. The alpha function may be viewed as the first difference of the nullity. We study the behavior of a under strong maps, and apply our results to proving Mason's alpha criterion: a matroid is the dual of a transversal matroid if and only if its alpha function is non