### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**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

Abstract:

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/