Permutations, moments, measures

Blitvic, Natasha and Steingrimsson, Einar (2020) Permutations, moments, measures. Transactions of the American Mathematical Society. ISSN 0002-9947 (In Press)

[img]
Text (BlitvicSteingrimsson_permutations_moments_measures)
BlitvicSteingrimsson_permutations_moments_measures.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.

Download (529kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Transactions of the American Mathematical Society
Additional Information:
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.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
147966
Deposited By:
Deposited On:
05 Oct 2020 09:00
Refereed?:
Yes
Published?:
In Press
Last Modified:
24 Oct 2020 06:54