Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Matthew Russell, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Set Partition Statistics: moment formulas and normality

Speaker: Robert C. Rhoades, Center for Communication Research, Princeton, NJ

Date: Thursday, October 2, 2014 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ


In studying the representation theory of certain finite groups we found that the 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. Motivated by this we have shown that there is a large algebra of other statistics with similar formulas for their moments. The coefficients in the linear combinations are polynomials in n. This allows exact enumeration of the moments for small n to determine exact formulas for all n. Computations led to the conjectured normality of many of these statistics. We used a stochastic algorithm for generating a random set partition due to Stam to establish the normality.

See: http://www.math.rutgers.edu/~russell2/expmath/