We consider a specialization YMβ(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 YMβ(1βp,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