论文标题
计数condorcet域
Counting Condorcet Domains
论文作者
论文摘要
Condorcet域是一系列线性订单的集合，可满足无环的多数关系。在本文中，我们将域名描述为定向汉密尔顿路径的集合。我们证明，尽管布莱克的单峰域是由其极端路径定义的，但箭头的单峰域却没有。我们还介绍了域收缩和域扩展以及自生域，并描述了这些域的某些特性。我们为自生域的数量而言，给出了箭头单峰域的同构类别的数量，并在此数字上给出上和下限。我们还列举了$ | a | = 5,6,7，8 $的独特最大箭头的单峰域。最后，我们表明，本文中的所有观察结果都可以翻译成单浸的域，即具有完整“ Never-Top”条件的Condorcet域。
A Condorcet domain is a collection of linear orders which satisfy an acyclic majority relation. In this paper we describe domains as collections of directed Hamilton paths. We prove that while Black's single-peaked domains are defined by their extremal paths, Arrow's single-peaked domains are not. We also introduce domain contractions and domain extensions as well as self-paired domains, and describe some properties of these. We give a formula for the number of isomorphism classes of Arrow's single-peaked domains in terms of the number of self-paired domains, and give upper and lower bounds on this number. We also enumerate the distinct maximal Arrow's single-peaked domains for $|A|=5,6,7, 8$. Finally, we show that all of the observations in this paper can be translated to single-dipped domains, that is, Condorcet domains with complete "never-top" conditions.
