Balanced Non-Transitive Dice II: Tournaments
Balanced Non-Transitive Dice II: Tournaments
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平衡非传递骰子 II：锦标赛
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Alex Schaefer
中科院分区：
文献类型：
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作者：
Alex Schaefer
我们进一步研究了标记骰子的集合，其中关系“是一个更好的骰子比”是非传递的。集中在一个额外的对称性，我们称之为“平衡”，我们证明了集$n$这样的$m$边骰子存在的所有$n，m \geq 3$。然后，我们将展示如何构建一组$n$骰子，使关系的行为根据箭头的方向的任何比赛（完全有向图）的$n$顶点。
We further study sets of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on sets with an additional symmetry we call "balance," we prove that sets of $n$ such $m$-sided dice exist for all $n,m \geq 3$. We then show how to construct a set of $n$ dice such that the relation behaves according to the direction of the arrows of any tournament (complete directed graph) on $n$ vertices.