Closed expressions for averages of set partition statistics

In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field, we found that the moments (mean, variance, and higher moments) of novel statistics on set partitions of [ n ]={1,2,⋯, n } have simple closed expressions as linear combinations of shi...

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Bibliographic Details
Published inResearch in the mathematical sciences Vol. 1; no. 1
Main Authors Chern, Bobbie, Diaconis, Persi, Kane, Daniel M, Rhoades, Robert C
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2014
Subjects
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Super Quality
Marked Partition
Bell Number
Dimension Exponent
Belated Shift
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Summary:In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field, we found that the moments (mean, variance, and higher moments) of novel statistics on set partitions of [ n ]={1,2,⋯, n } have simple closed expressions as linear combinations of shifted bell numbers. It is shown here that families of other statistics have similar moments. The coefficients in the linear combinations are polynomials in n . This allows exact enumeration of the moments for small n to determine exact formulae for all n .
ISSN:2197-9847
2197-9847
DOI:10.1186/2197-9847-1-2