Ranking and Unranking Restricted Permutations
Combinatorics
2025-09-30 v2
Abstract
We discuss efficient methods for unranking derangements and m\'enage permutations. That is, we will provide an algorithm to efficiently extract the -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.
Cite
@article{arxiv.2210.17021,
title = {Ranking and Unranking Restricted Permutations},
author = {Peter Kagey},
journal= {arXiv preprint arXiv:2210.17021},
year = {2025}
}