2021
DOI: 10.1090/tran/8330
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Permutations, Moments, Measures

Abstract: Which combinatorial sequences correspond to moments of probability measures on the real line? We present a generating function, in the form of a continued fraction, for a fourteenparameter family of such sequences and interpret these in terms of combinatorial statistics on the symmetric groups. Special cases include several classical and noncommutative probability laws, along with a substantial subset of the orthogonalizing measures in the q-Askey scheme, now given a new combinatorial interpretation in terms o… Show more

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Cited by 4 publications
(1 citation statement)
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“…Considering families built around more general hypergeometric functions, the quadrabasic Hermite sequence belongs to the octabasic Laguerre family (or its symmetric version) introduced by Simion and Stanton [43] and recently extended by Blitvić and Steingrímsson [12] or Sokal and Zeng [44] (see also the earlier work [39]). This formula recovers the hyperbolic secant case when q = t = v = w = 1.…”
mentioning
confidence: 99%
“…Considering families built around more general hypergeometric functions, the quadrabasic Hermite sequence belongs to the octabasic Laguerre family (or its symmetric version) introduced by Simion and Stanton [43] and recently extended by Blitvić and Steingrímsson [12] or Sokal and Zeng [44] (see also the earlier work [39]). This formula recovers the hyperbolic secant case when q = t = v = w = 1.…”
mentioning
confidence: 99%