Ranking and Unranking Restricted Permutations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909813608284160 |
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| author | Kagey, Peter |
| author_facet | Kagey, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17021 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ranking and Unranking Restricted Permutations Kagey, Peter Combinatorics 05A05 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. |
| title | Ranking and Unranking Restricted Permutations |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2210.17021 |