Permutations, moments, measures

Blitvic, Natasha and Steingrimsson, Einar (2020) Permutations, moments, measures. arXiv.

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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 Askey-Wilson 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:
arXiv
ID Code:
141760
Deposited By:
Deposited On:
24 Feb 2020 09:25
Refereed?:
No
Published?:
Published
Last Modified:
25 Jun 2020 04:28