恰有t行含s圈正元的布尔方阵的幂敛指数

Convergent Indices of Boolean Matrices with s Cycle Positive Elements on Exactly t Rows

设Ｄｎ，ｓ（ｔ）是恰有ｔ行含ｓ圈正元的ｎ阶布尔方阵的集合，ｓｔｎ．本文给出了当ｓ＝１或ｓ为素数时Ｄｎ，ｓ（ｔ）中矩阵的幂敛指数的一个上界，证明了除ｔ＞ｎ－ｓ（ｎ－１）＋１／４－３／２，且ｓ与ｎ不互素外，这个上界可以达到，对Ｄｎ，ｓ（ｔ）中幂敛指数达到这个上界的矩阵作了部分刻划．

Let D n,s (t) be the set of n by n Boolean matrices with s-cycle positive elements on exactly t rows, stn. We derive a upper bound for the convergent indices of matrices in D n,s (t) when s=1 or s is prime. We prove that this upper bound can be attained except the case that t>n-s(n-1)+1/4-3/2, and s and n are not comprime. And we give partial characterizations of the matrices in D n,s (t) whose convergent indices attain this upper bound.