The Tutte polynomial of a morphism of matroids — 5. Derivatives as generating functions of Tutte activities

We show that in an ordered matroid the partial derivative ∂ p + q t / ∂ x p ∂ y q of the Tutte polynomial is p ! q ! times the generating function of activities of subsets with corank p and nullity q . More generally, this property holds for the 3-variable Tutte polynomial of a matroid perspective.