THE TUTTE DICHROMATE AND WHITNEY HOMOLOGY OF MATROIDS

DAVID G. WAGNER

Abstract. We consider a specialization Y_{M}(q, t) of the Tutte polynomial of a matroid M which is inspired by analogy with the Potts model from statistical mechanics. The only information lost in this specialization is the number of loops of M. We show that the coefficients of Y_{M}(1 − p, t) are very simply related to the ranks of the Whitney homology groups of the opposite partial orders of the independent set complexes of the duals of the truncations of M. In particular, we obtain a new homological interpretation for the coefficients of the characteristic polynomial of a matroid.