Abstract.
Given a probability distribution on a totally ordered set, we define for each \( n \geq 1 \) a related distribution on the symmetric group \( \frak S_n \), called the QS-distribution. It is a generalization of the q-shuffle distribution considered by Bayer, Diaconis, and Fulman. The QS-distribution is closely related to the theory of quasisymmetric functions and symmetric functions. We obtain explicit formulas in terms of quasisymmetric and symmetric functions for the probability that a random permutation from the QS-distribution satisfies various properties, such as having a given descent set, cycle structure, or shape under the Robinson-Schensted-Knuth algorithm.
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Received March 28, 2001
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Stanley, R. Generalized Riffle Shuffles and Quasisymmetric Functions. Annals of Combinatorics 5, 479–491 (2001). https://doi.org/10.1007/s00026-001-8023-7
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DOI: https://doi.org/10.1007/s00026-001-8023-7