Sums of permanental minors using Grassmann algebra
  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. 
P. Butera (Univ. Milano-Bicocca Phys. Dept. and INFN) and M. Pernici   (INFN and Univ. of Milano Phys. Dept)
hep-lat math-ph math.MP