Let B<sub>n</sub> denote the set of n×n Boolean matrices. For A=(a<sub>ij</sub>), B=(b<sub>ij</sub>)∈B<sub>n</sub>, if a<sub>ij</sub>≤b<sub>ij&l...Let B<sub>n</sub> denote the set of n×n Boolean matrices. For A=(a<sub>ij</sub>), B=(b<sub>ij</sub>)∈B<sub>n</sub>, if a<sub>ij</sub>≤b<sub>ij</sub>, i. j= 1, 2, '', n. we say A≤B. An n×n Boolean matrix A is called primitive if there exists some positive integer k such that A<sup>k</sup>=J<sub>n</sub>, the all l’s matrix in B<sub>n</sub>. Such a least positive integer k is called the exponent of A, denoted by γ（A）. Let P<sub>n</sub> denote the set of all n×n primitive matrices in B<sub>n</sub>. A matrix A∈B<sub>n</sub> is called a Hall matrix if there exists some permutation matrix Q such that Q≤A.展开更多
文摘Let B<sub>n</sub> denote the set of n×n Boolean matrices. For A=(a<sub>ij</sub>), B=(b<sub>ij</sub>)∈B<sub>n</sub>, if a<sub>ij</sub>≤b<sub>ij</sub>, i. j= 1, 2, '', n. we say A≤B. An n×n Boolean matrix A is called primitive if there exists some positive integer k such that A<sup>k</sup>=J<sub>n</sub>, the all l’s matrix in B<sub>n</sub>. Such a least positive integer k is called the exponent of A, denoted by γ（A）. Let P<sub>n</sub> denote the set of all n×n primitive matrices in B<sub>n</sub>. A matrix A∈B<sub>n</sub> is called a Hall matrix if there exists some permutation matrix Q such that Q≤A.
