  We show that a formalism proposed by Creutz to evaluate Grassmann integrals
provides an algorithm of complexity $O(2^n n^3)$ to compute the generating
function for the sum of the permanental minors of a matrix of order $n$. This
algorithm improves over the Brualdi-Ryser formula, whose complexity is at least
$O(2^{\frac{5n}{2}})$. In the case of a banded matrix with band width $w$ and
rank $n$ the complexity is $O(2^{min(2w, n)} (w + 1) n^2)$. Related algorithms
for the matching and independence polynomials of graphs are presented.
