Characteristic Polynomial as a Tutte Polynomial Specialization is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a finite matroid on ground set , with rank function . Let denote its Tutte polynomial, and let denote its characteristic polynomial. Then \begin{align } \chi M(q)=( 1)^{r(E)}T M(1 q,0). \end{align.