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Coherent random permutations with record statistics

Abstract : A two-parameter family of random permutations of $[n]$ is introduced, with distribution conditionally uniform given the counts of upper and lower records. The family interpolates between two versions of Ewens' distribution. A distinguished role of the family is determined by the fact that every sequence of coherent permutations $(π _n,n=1,2,\ldots)$ with the indicated kind of sufficiency is obtainable by randomisation of the parameters. Generating algorithms and asymptotic properties of the permutations follow from the representation via initial ranks.
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Alexander Gnedin. Coherent random permutations with record statistics. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.157-170. ⟨hal-01184799⟩

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