用Grassmann代数求积式和
Sums of permanental minors using Grassmann algebra
摘要：
我们表明，Creutz提出的形式主义，以评估格拉斯曼积分提供了一个算法的复杂性$O(2^n n^3)$计算生成函数的总和的永久未成年人的矩阵的顺序$n$。该算法改进了Brualdi-Ryser公式，其复杂度至少为$O(2^{\frac{5n}{2}})$ .在具有带宽$w$和秩$n$的带状矩阵的情况下，复杂度为$O(2^{min(2w, n)} (w + 1) n^2)$。给出了图的匹配多项式和图的独立多项式的相关算法。
英文摘要：
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.
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