| 恰有t行含s圈正元的布尔方阵的幂敛指数 |
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| 引用本文： | 周波,柳柏濂.恰有t行含s圈正元的布尔方阵的幂敛指数[J].数学学报,1998,41(3):517-524. |
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| 作者姓名： | 周波 柳柏濂 |
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| 作者单位： | 华南师范大学数学系 |
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| 摘 要： | 设Ｄｎ，ｓ（ｔ）是恰有ｔ行含ｓ圈正元的ｎ阶布尔方阵的集合，ｓｔｎ．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．
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| 关 键 词： | 布尔矩阵，幂敛指数，s圈正元，有向图 |
| 收稿时间： | 1996-4-3 |
Convergent Indices of Boolean Matrices with s Cycle Positive Elements on Exactly t Rows |
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| Zhou Bo,Liu Bolian.Convergent Indices of Boolean Matrices with s Cycle Positive Elements on Exactly t Rows[J].Acta Mathematica Sinica,1998,41(3):517-524. |
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| Authors: | Zhou Bo Liu Bolian |
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| Institution: | Zhou Bo Liu Bolian (Department of Mathematics, South China Normal University, Guangzhou 510631, China) (Fax: (020) 85211340, Email:Liubl@hsut.scnu.edu.cn) |
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| Abstract: | Let D n,s (t) be the set of n by n Boolean matrices with s-cycle positive elements on exactly t rows, stn. 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. |
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| Keywords: | Boolean matrix Convergent index s-Cycle positive elements Digraph |
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