Permutations, moments, measures

Blitvic, Natasha and Steingrimsson, Einar (2021) Permutations, moments, measures. Transactions of the American Mathematical Society. 0-0. ISSN 0002-9947

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We present a continued fraction with 13 permutation statistics, several of them new, connecting a great number of combinatorial structures to a wide variety of moment sequences and their measures from classical and noncommutative probability. The Hankel determinants of these moment sequences are a product of (p,q)-factorials, unifying several instances from the literature. The corresponding measures capture as special cases several classical laws, such as the Gaussian, Poisson, and exponential, along with further specializations of the orthogonalizing measures in the q-Askey scheme and several known noncommutative central limits. Statistics in our continued fraction generalize naturally to signed and colored permutations, and to the k-arrangements introduced here, permutations with k-colored fixed points.

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Journal Article
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Transactions of the American Mathematical Society
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First published in Transactions of the American Mathematical Society in [volume/issue number and year], published by the American Mathematical Society. © 2020 American Mathematical Society.
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05 Oct 2020 09:00
Last Modified:
02 Mar 2021 09:16