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.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2006年第5期641-646,共6页
Acta Mathematica Scientia
基金
韩国Com~2MaC-KOSEF基金资助
关键词
布尔矩阵
幂敛指数
周期
有向图
圈
Boolean matrix
Index of convergence
Period
Digraph
Cycle
