Transversal theory and F-products

Brown, Terrence J.

doi:10.1016/0097-3165(74)90094-6

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The Alpha Function of a Matroid—I. Transversal Matroids

Kung

1978

Stud Appl Math

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Let n be the nullity function of the matroid G(S). The Mason alpha function is defined on subsets A of S by the recursion α(A)=n(A)−∑F⊂Aα(F), the summation being over all flats F strictly contained in A. 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‐negative.

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