Some properties of the permanent of (1, -1)-matrices
Some properties of the permanent of (1, -1)-matrices
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(1, -1)-矩阵的永久矩阵的一些性质
DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
N. Seifter
中科院分区：
文献类型：
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作者：
Arnold R. Kräuter;N. Seifter
令ω n表示所有n × n −（1，−1）-矩阵的集合。[5] E. I.二.王提出如下问题。当A ω n非奇异时，[per A]有一个合适的上限吗？本文猜想最佳可能界是ω n中矩阵的积和式，该矩阵恰好包含n1个负元素，且所有负元素都出现在其主对角线上。这一猜想通过对Ω n中一大类矩阵的研究得到了证实。此外，还得到了Ω n中关于持久函数的一些有趣的结果.
Let ω n denote the set of all n × n −(1, −1)-matrices. In [5] E. I. II. Wang posed the following problem. Is there a decent upper bound for [per A] when A ∊ ω n is nonsingular? In this paper we conjecture that the best possible bound is the permanent of a matrix in ω n which contains exactly n 1 negative entries all occurring in its main diagonal. This conjecture is affirmed by the study of a large class of matrices in Ω n . Moreover, some other interesting results concerning the permanent function in Ω n are given.