马红平,苗正科.一类二元关系的公共后继指数集[J].数学研究及应用,2008,28(3):460~466 |
一类二元关系的公共后继指数集 |
On the Set of Common Consequent Indices of a Class of Binary Relations |
投稿时间:2006-07-19 修订日期:2006-12-12 |
DOI:10.3770/j.issn:1000-341X.2008.03.002 |
中文关键词: 公共后继指数 本原关系 有向图. |
英文关键词:common consequent index primitive relation directed graph. |
基金项目:江苏省自然科学基金(No.BK2007030); 江苏省高校自然科学基金(No.07KJD110207). |
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中文摘要: |
设$V=\{ a_{1},a_{2},\ldots ,a_{n}\}$是$n\geq 2$的一个有限集合,$V$上所有本原的二元关系组成的集合记为$P_{n}(V)$.对任意的$Q\in P_{n}(V)$,与$Q$对应的有向图记为$G(Q)$.记$ P_{n}(V,d)=\{Q:Q\in P_{n}(V)$ 且$G(Q)$ 恰好包含 $d$ 个环\},其中$0
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英文摘要: |
Let $V=\{ a_{1},a_{2},\ldots,a_{n}\} $ be a finite set with $n\geq 2$ and $P_{n}(V)$ the set of all primitive binary relations on $V$. For $Q\in P_{n}(V)$, denote by $G(Q)$ the directed graph corresponding to $Q$. For positive integer $d\leq n$, let $ P_{n}(V,d)=\{Q:Q\in P_{n}(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 $P_{n}(V,d)$ is $\{1,2,\ldots,n-\lceil \frac{d}{2}\rceil \}$. Furthermore, the minimal extremal binary relations are described. |
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