论文标题
关于圆形足球比赛的得分表的一致性
On the consistency of score sheets of a round-robin football tournament
论文作者
论文摘要
在本文中，我们介绍了submonoids $ \ mathscr {r} _n $，resp。 $ \ mathscr {c} _n $，是monoid $ \ mathscr {m} _n $的订单得分表的订单得分表，由$ n $ n $ teams参加，在领导者团队被取消资格之后，该订单保留了订单。所有主要的一务件都保留给定的订单。我们研究（同时使用理论和计算方法）这些单体最重要的不变性，即希尔伯特的基础，多样性，希尔伯特系列和希尔伯特功能。特别是，我们对$ \ mathscr {r} _n $的希尔伯特基础的一般描述，我们证明$ \ mathscr {c} _n $是gorenstein，是$ n> 2 $。
In this paper we introduce the submonoids $\mathscr{R}_n$, resp. $\mathscr{C}_n$, of the monoid $\mathscr{M}_n$ of ordered score sheets of a robin-round tournament played by $n$ teams for which the order is preserved after the leader team is disqualified, resp. all principal submatrices preserve the given ordering. We study (using both theoretical and computational methods) the most important invariants of these monoids, namely the Hilbert basis, the multiplicity, the Hilbert series and the Hilbert function. In particular we give a general description of the Hilbert basis of $\mathscr{R}_n$ and we show that $\mathscr{C}_n$ is Gorenstein for $n>2$.
