Maximally Nontransitive Dice
Maximally Nontransitive Dice
复制标题
最大非传递骰子
DOI：
10.1080/00029890.2018.1427392
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
A. Hales
中科院分区：
文献类型：
--
作者：
J. Buhler;Ron Graham;A. Hales
摘要构造具有显著非传递性的任意大骰子集。从某种意义上说，每个集合都通过将不同的掷骰次数相加来展示所有可能的成对赢/输关系。这个事实的证明依赖于多次掷骰子的和的中位数和平均值之差的渐近公式。这个公式是一个合适的Edgeworth级数（中心极限定理的渐近改进）的结果，我们在最后一节给出了一个详细的证明草图。
Abstract We construct arbitrarily large sets of dice with some remarkable nontransitivity properties. In a sense made precise later, each set exhibits all possible pairwise win/loss relationships by summing different numbers of rolls. The proof of this fact relies on an asymptotic formula for the difference between the median and mean of sums of multiple rolls of dice. This formula is a consequence of a suitable Edgeworth series (an asymptotic refinement of the central limit theorem), for which we give a detailed sketch of a proof in the final section.