图论 - 锦标赛排名
给定一个像这样的锦标赛图： 如何系统地找出有多少个排名？ 帮助/解释将不胜感激。
Given a tournament graph like this :
How do you find out how many rankings there are systematically?
Help / explanation would really be appreciated.
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您是否特指此图，其中每个节点都有两个“入”边和两个“出”边？也就是说，没有理由选择任何特定节点的图表，并且五个字母的任何排列都同样好？这只是问你可以用多少种不同的方式排列五个字母。
顺便说一句，这个图表让我很想起石头、剪刀、布、史波克、蜥蜴的输赢图表。事实上，如果您将
x识别为纸，y识别为蜥蜴，v识别为剪刀，w，您就会得到此图> 与 Spock，u与 rock。如果a击败b，就会有一个从a到b的箭头。Did you mean this graph specifically, in which every node has two "in" edges and two "out" edges? That is, a graph in which there's no reason to prefer any specific node, and any arrangement of five letters is equally good? That's just asking how many different ways you can arrange five letters.
As an aside, the graph reminds me very much of the win-lose graph of Rock, Paper, Scissors, Spock, Lizard. In fact, you get this graph if you identify
xwith paper,ywith lizard,vwith scissors,wwith Spock, anduwith rock. There is an arrow fromatobifadefeatsb.