Single-peakedness was introduced by Black (J Political Econ 56:23–34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published in recent years, and some observations of known results and examples by the author. The underlying basic structure of tiling type and properties of single-peaked domains provided here give a good visualization and make further developments on single-peakedness more easy.

中文翻译：

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通过递归切片轻松构建完整的单峰域

布莱克（J政治经济学56：23–34，1948年）引入了单峰作为克服Condorcet悖论的充分条件。从那时起，它一直吸引着各个领域的研究人员的兴趣。在本文中，我们结合最近几年发表的两个结果，以及作者对已知结果和示例的一些观察，提出了一个简单的递归过程，该过程可为任何有限的替代集显式构建完整的平铺型单峰域。此处提供的切片类型的底层基本结构和单峰域的属性可提供良好的可视化效果，并使对单峰性的进一步开发更加容易。