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.
Accepted author manuscript, 517 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Accepted author manuscript, 615 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Submitted manuscript
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Permutations, moments, measures
AU - Blitvic, Natasha
AU - Steingrimsson, Einar
N1 - First published in Transactions of the American Mathematical Society in 374/8 (2021), published by the American Mathematical Society. © 2020 American Mathematical Society.
PY - 2021/8/31
Y1 - 2021/8/31
N2 - 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.
AB - 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.
U2 - 10.1090/tran/8330
DO - 10.1090/tran/8330
M3 - Journal article
VL - 374
SP - 5473
EP - 5508
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -