Peak-Pit Condorcet域的Danilov-Karzanov-Koshevoy构造的推广
Generalisation of the Danilov-Karzanov-Koshevoy Construction for Peak-Pit Condorcet Domains
摘要：
Danilov，Karzanov and Koshevoy（2012）几何上引入了一个有趣的拼接Condorcet域的复合运算，并利用它反驳了Fishburn关于连通Condorcet域的最大尺寸的一个长期存在的问题。我们给出了这个操作的代数定义，并研究了它的性质。本文给出了两个Condorcet域的复合势的精确公式，改进了Danilov，Karzanov和Koshevoy的结果，证明了Fishburn的交替方案并不总是定义一个最大的峰坑Condorcet域.
英文摘要：
Danilov, Karzanov and Koshevoy (2012) geometrically introduced an interesting operation of composition on tiling Condorcet domains and using it they disproved a long-standing problem of Fishburn about the maximal size of connected Condorcet domains. We give an algebraic definition of this operation and investigate its properties. We give a precise formula for the cardinality of composition of two Condorcet domains and improve the Danilov, Karzanov and Koshevoy result showing that Fishburn's alternating scheme does not always define a largest peak-pit Condorcet domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
