On matroids determined by their Tutte polynomials Original Research Article

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 image and of the truncations of image, and we show the existence of exponentially large families of T-unique matroids.