论文标题
排名和不合格的限制排列
Ranking and Unranking Restricted Permutations
论文作者
论文摘要
我们讨论了无关乱和梅纳奇排列的有效方法。也就是说，我们将提供一种算法来有效提取$ k $ - 在词典订购下最早的置换。我们将证明，可以将这个问题简化为计算给定前缀限制排列数量的问题，然后我们将使用ROK理论来解决此计数问题。这具有组合，概率，统计和建模的应用程序。
We discuss efficient methods for unranking derangements and ménage permutations. That is, we will provide an algorithm to efficiently extract the $k$-th earliest such permutation under the lexicographic ordering. We will show that this problem can be reduced to the problem of computing the number of restricted permutations with a given prefix, and then we will use rook theory to solve this counting problem. This has applications to combinatorics, probability, statistics, and modeling.
