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arXiv · 2210.17021

Ranking and Unranking Restricted Permutations

Peter Kagey
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Abstract

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.

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BibTeXRIS

Peter Kagey. 2023-11-09. Ranking and Unranking Restricted Permutations. https://doi.org/10.1016/j.dam.2024.05.010

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