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  • BlitvicSteingrimsson_permutations_moments_measures

    Rights statement: 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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    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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Permutations, moments, measures

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<mark>Journal publication date</mark>31/08/2021
<mark>Journal</mark>Transactions of the American Mathematical Society
Issue number8
Volume374
Number of pages36
Pages (from-to)5473-5508
Publication StatusPublished
Early online date5/01/21
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

First published in Transactions of the American Mathematical Society in 374/8 (2021), published by the American Mathematical Society. © 2020 American Mathematical Society.