一类二元关系的公共后继指数集

一类二元关系的公共后继指数集

Let V = {α1, α2,…, αn} be a finite set with n ≥ 2 and Pn(V) the set of all primitive binary relations on V. For Q ∈ Pn(V), denote by G(Q) the directed graph corresponding to Q.For positive integer d ≤ n, let Pn(V, d) = {Q:Q ∈ Pn(V) and G(Q) contains exactly d loops}. In this paper, it is proved that the set of common consequent indices of binary relations in Pn(V, d) is {1, 2 , n - [d/2]}. Furthermore, the minimal extremal binary relations are described.

作 者： 马红平 苗正科 MA Hong Ping MIAO Zheng Ke   作者单位： 马红平,MA Hong Ping(School of Mathematical Sciences, Xuzhou Normal University, Jiangsu 221116, China)

苗正科,MIAO Zheng Ke(School of Mathematical Sciences, Xuzhou Normal University, Jiangsu 221116, China;Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Science, Beijing 100080, China) 

刊 名： 数学研究与评论  ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION  年，卷(期)： 2008 28(3)  分类号： O157.5  关键词： common consequent index   primitive relation   directed graph  

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