Double-Elimination Tournaments: Counting and Calculating
Double-Elimination Tournaments: Counting and Calculating
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双败淘汰赛：计数和计算
DOI：
10.1080/00031305.1996.10473538
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
C. T. Edwards
中科院分区：
文献类型：
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作者：
C. T. Edwards
摘要巡回赛是体育赛事中选拔冠军的一种常用手段。它们也用于需要配对比较程序的实验中。淘汰赛是最有用的时候，治疗的数量太大，使用更知名的循环赛。数学和统计文献并没有解决这样的问题，如一个人应该如何在锦标赛中的种子球队或锦标赛结构是适当的。对于双淘汰赛（DE），即使是基本的问题，如有多少结构仍然没有答案。本文讨论了关于DE锦标赛的一些基本问题，包括DE锦标赛的数量和球队赢得DE锦标赛的概率。爱德华兹给出了许多关于单淘汰赛（SE）的结果，例如赢得SE锦标赛的概率以及标记和计数它们的符号。在这篇文章中，我为DE锦标赛开发了类似的结果。所得结果适用于一个arb…
Abstract Tournaments are popularly used in sporting events to select a champion. They are also used in experiments where paired comparison procedures are needed. Knockout tournaments are most useful when the number of treatments is too large to use the more well-known round-robin tournament. The mathematical and statistical literature does not address questions such as how one should seed teams in a tournament or which tournament structures are appropriate. For double-elimination (DE) tournaments even basic questions such as how many structures there are remain unanswered. This article addresses some fundamental questions concerning DE tournaments, including the number of DE tournaments and the probabilities of teams winning a DE tournament. Edwards gives many results about single-elimination (SE) tournaments, such as the probability of winning an SE tournament and a notation for labeling and counting them. In this article I develop similar results for the DE tournaments. The results given apply to an arb...