一类非对称矩阵的最大密度指数集

The Index Set of Maximum Density for a Class of Non-symmetric Matrix

证明了至少有一对非零对称元但非对称且周期为2的n阶非本原不可约布尔矩阵所成的类的最大密度指数集是:(ⅰ)若n(>3)是偶数,则Hn={2,3,4,5,…,2n-5,2n-4};(ⅱ)若n(>3)是奇数,则Hn={m∶2≤m≤2n-4且2｜m}.

In this paper,the author completely determines the index set of maximum density for the class of n order nonsymmetric imprimitive irreducible Boolean matrix with at least one pair of nonzero symmetry entries and whose given period is two. The main results are the following :(ⅰ)if n(>3) is even, then Hn={2,3,4,5,...,2n-5,2n-4};(ⅱ)if n(>3) is odd, then  Hn={m∶2≤m≤2n-4 and m is even}.