广义不及物骰子II:分治结构

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
E. Akin, Julia Saccamano
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引用次数: 5

摘要

广义$N$边模是$N$样本空间上的随机变量$D$,其结果取正整数集中的值的可能性相等。对于独立的$N$边骰子$D_i,D_j$,如果$Probe(D_i>D_j)>\frac{1}{2}$,则$D_i$胜过$D_j$。骰子$\{D_i:i=1,\dots,n \}$的集合在集合$[n]=\{1,2,\dotsn \}$上建模锦标赛,即当锦标赛中$D_i\到D_j$当且仅当$i\到j$时,具有$n$顶点的完全有向图。通过使用集合$[Nn]$的$n$折叠分区和每个大小为$n$的集合,我们可以对$[n]$上的任意锦标赛进行建模。通过$N=3^{N-2}$的例子,得到了所需大小$N$的界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generalized intransitive dice II: Partition constructions
A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i \to D_j$, if $Prob(D_i > D_j) > \frac{1}{2} $. A collection of dice $\{ D_i : i = 1, \dots, n \}$ models a tournament on the set $[n] = \{ 1, 2, \dots, n \}$, i.e. a complete digraph with $n$ vertices, when $D_i \to D_j$ if and only if $i \to j$ in the tournament. By using $n$-fold partitions of the set $[Nn] $ with each set of size $N$ we can model an arbitrary tournament on $[n]$. A bound on the required size of $N$ is obtained by examples with $N = 3^{n-2}$.
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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