On matroids determined by their Tutte polynomials

A matroid is T-unique if it is determined up to isomorphism by its Tutte polynomial. Known T-unique matroids include projective and affine geometries of rank at least four, wheels, whirls, free and binary spikes, and certain generalizations of these matroids. In this paper we survey this work and give three new results. Namely, we prove the T-uniqueness of M(Km,n) and of the truncations of M(Kn), and we show the existence of exponentially large families of T-unique matroids.