论文标题
平衡的非转换骰子的可能性和不可约性
Possible probability and irreducibility of balanced non-transitive dice
论文作者
论文摘要
我们为任何正整数$ n $构建了不可约合的$ n $侧面骰子的不可总体平衡的集合，该集合在\ cite [Question 5.2] {ss17}中提出。该建筑的一种主要工具是研究所谓的公平骰子。此外，我们还研究了平衡的非交易骰子集骰子概率的分布。 For a lower bound, we show that the probability could be arbitrarily close to $\frac{1}{2}$ and for a upper bound, we construct a balanced non-transitive set of dice whose probability is $\frac{1}{2} + \frac{13-\sqrt{153}}{24} \approx \frac{1}{2} + \ frac {1} {9.12}。$
We construct irreducible balanced non-transitive sets of $n$-sided dice for any positive integer $n$, which was raised in \cite[Question 5.2]{SS17}. One main tool of the construction is to study so-called fair sets of dice. Furthermore, we also study the distribution of the probabilities of balanced non-transitive sets of dice. For a lower bound, we show that the probability could be arbitrarily close to $\frac{1}{2}$ and for a upper bound, we construct a balanced non-transitive set of dice whose probability is $\frac{1}{2} + \frac{13-\sqrt{153}}{24} \approx \frac{1}{2} + \frac{1}{9.12}.$
