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Article Dans Une Revue Discrete Mathematics Année : 2021

Central limit theorem for the prefix exchange distance under Ewens sampling formula

Résumé

The prefix exchange distance of a permutation is the length of its shortest factorisation into transpositions that all contain 1. Using a probabilistic approach, we obtain expressions for the mean and the variance, and prove the asymptotic normality of the distribution of this distance for a random permutation verifying the Ewens sampling formula. Analogous results in the uniform setting follow as simple corollaries.
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Dates et versions

hal-02494137 , version 1 (28-02-2020)

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Simona Grusea, Anthony Labarre. Central limit theorem for the prefix exchange distance under Ewens sampling formula. Discrete Mathematics, 2021, 344 (2), pp.Article 112206. ⟨10.1016/j.disc.2020.112206⟩. ⟨hal-02494137⟩
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