具有确定非零对角元个数的布尔矩阵广义幂敛指数的极矩阵  

The Extremal Matrices of Generalized Indices of Convergence of Boolean Matrices with Given Number of Non-zero Diagonal Entries

作　　者：周波[1] 

机构地区：[1]华南师范大学数学系,广州510631

出　　处：《数学学报（中文版）》2005年第1期17-24,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10201009)广东省自然科学基金资助项目(021072)

摘　　要：设A是周期为P的n阶布尔矩阵,1≤i≤n,A的广义幂敛指数k(A,i)是使得Ak和Ak+p有i行对应相等的最小非负整数k.本文刻画了恰含d(1≤d≤n)个非零对角元的n阶布尔矩阵的广义幂敛指数的极矩阵.Let A be an n x n Boolean matrix with period p, 1≤i≤n. The generalized index of convergence k(A, i) of A is the least nonnegative integers k such that i rows of Ak and Ak+p are mutually equal. We characterize the extremal matrices of generalized indices of convergence of the n×n Boolean matrices with exactly d (1≤d≤n) non-zero diagonal entries.

关 键 词：幂敛指数 布尔矩阵 对角元 刻画 个数 广义 相等 对应 周期 整数 

分 类 号：O157.5[理学—数学] O151.21[理学—基础数学]