关于循环赛中胜者得分的分布
On the distribution of winners' scores in a round-robin tournament
AI总结：
研究经典循环赛中选手排名得分的分布，针对一般 $n$ 无法获得精确分布的问题，推导出了其极限分布。
摘要：
在经典国际象棋循环赛中，$n$ 名选手与其他 $n-1$ 名选手比赛，每局结果为胜、平或负。胜者得 1 分，平局得 1/2 分，负者得 0 分。我们研究 ${\displaystyle {n \choose 2}}$ 局比赛后 $n$ 名选手排名得分的分布，即最高分、次高分等的分布。一般 $n$ 的精确分布似乎无法获得；我们求得了极限分布。
英文摘要：
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of $n$ players after ${\displaystyle {n \choose 2}}$ games, i.e. the distribution of the maximal score, second maximum, and so on. The exact distribution for a general $n$ seems impossible to obtain; we obtain a limit distribution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
