论文标题
计数比赛得分序列
Counting tournament score sequences
论文作者
论文摘要
比赛的得分顺序是其以非续顺序排列的顶点的序列。计数与$ N $顶点的比赛的分数序列的问题超过100年（Macmahon 1920）。 2013年，汉娜（Hanna）猜想了这些数字令人惊讶且优雅的递归。我们通过证明它是我们的主要定理的推论，在肯定中解决了这一猜想，这是用划分索引的得分序列生成函数的分解。我们还得出了用于计数得分序列的封闭公式和二次时间算法。
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In 2013 Hanna conjectured a surprising and elegant recursion for these numbers. We settle this conjecture in the affirmative by showing that it is a corollary to our main theorem, which is a factorization of the generating function for score sequences with a distinguished index. We also derive a closed formula and a quadratic time algorithm for counting score sequences.
