Limit theorems are proved for fixed points, descents, and inversions under iterated random-to-top shuffles, with new combinatorial proofs resolving open questions on expectations.
Fulman,The distribution of descents in fixed conjugacy classes of the symmetric groups, Journal of Combina- torial Theory, Series A84(1998), 171–180
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On the statistics of random-to-top shuffles
Limit theorems are proved for fixed points, descents, and inversions under iterated random-to-top shuffles, with new combinatorial proofs resolving open questions on expectations.