A new generation tree for permutations, preserving the number of fixed points
We describe a new uniform generation tree for permutations with the specific property that, for most permutations, all of their descendants in the generation tree have the same number of fixed points. Our tree is optimal for the number of permutations having this property. We then use this tree to d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2014-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2433/pdf |
| Summary: | We describe a new uniform generation tree for permutations with the specific property that, for most permutations, all of their descendants in the generation tree have the same number of fixed points. Our tree is optimal for the number of permutations having this property. We then use this tree to describe a new random generation algorithm for derangements, using an expected n+O(1) calls to a random number generator. Another application is a combinatorial algorithm for exact sampling from the Poisson distribution with parameter 1. |
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| ISSN: | 1365-8050 |