Asymptotic behavior of permutation records |
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Authors: | Igor Kortchemski |
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Affiliation: | École Normale Supérieure, 75005 Paris, France |
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Abstract: | We study the asymptotic behavior of two statistics defined on the symmetric group Sn when n tends to infinity: the number of elements of Sn having k records, and the number of elements of Sn for which the sum of the positions of their records is k. We use a probabilistic argument to show that the scaled asymptotic behavior of these statistics can be described by remarkably simple functions. |
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Keywords: | Records Stirling numbers Scaled asymptotic behavior Independent random variables |
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