含s-圈布尔矩阵类的幂敛指数集  

On the Set of Indices of Convergence for the Class of s-Cycle Boolean Matrices

作　　者：周波[1] Han Hyuk Cho Suh Ryung Kim 

机构地区：[1]华南师范大学数学系,广州510631 [2]首尔大学数学教育系

出　　处：《数学物理学报（A辑）》2006年第5期641-646,共6页Acta Mathematica Scientia

基　　金：韩国Com~2MaC-KOSEF基金资助

摘　　要：在布尔运算下,布尔矩阵A的幂敛指数和周期分别是使A^k=A^(k+p)成立的最小非负整数k和最小正整数p．人们对周期的认识已经相当完善．给定满足一个不等式的正整数n和s,利用组合分析确定了有向图含至少一个s-圈的n×n布尔矩阵的幂敛指数可以取得的数值．Using Boolean arithmetic, the index of convergence and period of a Boolean matrix A are respectively the least non-negative integer k and the least positive integer p respectively such that A^k - A^k＋p. The knowledge about the period is quite completed. Given positive integers n and s satisfying a certain inequality, the authors apply combinatorial arguments to determine which numbers are attainable as the indices of convergence of n × n Boolean matrices whose digraphs contain at least one s-cycle.

关 键 词：布尔矩阵 幂敛指数 周期 有向图 圈 

分 类 号：O157[理学—数学]