论文标题
如何设计稳定的连续淘汰赛比赛
How to Design a Stable Serial Knockout Competition
论文作者
论文摘要
我们研究了一种新的比赛格式，该格式包括一系列单独的淘汰赛。我们将这种新格式称为连续淘汰赛（SKC）。这种格式最近已被专业飞镖公司采用。根据每场淘汰赛的球员的种子，球员都可以在淘汰赛中的各个回合（例如第一轮，第二轮，第二轮，半决赛，决赛）见面。遵循公平对待所有球员平等的原则，我们确定了SKC的有吸引力的特性：每对SKC的每一轮都应该经常相等地相遇。如果种子确实存在该特性，我们将其称为由此产生的SKC稳定。在本说明中，我们将此概念形式化，我们解决了一个问题：每个淘汰赛都有种子，以使所得的SKC稳定吗？我们显示，使用与Fano平面的连接，对于8个玩家来说，答案是肯定的。我们展示了如何将其推广到2个力量的任何球员，我们为16和32名球员的比赛提供了稳定的时间表
We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a Serial Knockout Competition (SKC). This format has recently been adopted by the Professional Darts Corporation. Depending on the seedings of the players used for each of the knockout tournaments, players can meet in the various rounds (eg first round, second round, ..., semi-final, final) of the knockout tournaments. Following a fairness principle of treating all players equal, we identify an attractive property of an SKC: each pair of players should potentially meet equally often in each of the rounds of the SKC. If the seedings are such that this property is indeed present, we call the resulting SKC stable. In this note we formalize this notion, and we address the question: do there exist seedings for each of the knockout tournaments such that the resulting SKC is stable? We show, using a connection to the Fano plane, that the answer is yes for 8 players. We show how to generalize this to any number of players that is a power of 2, and we provide stable schedules for competitions on 16 and 32 players
