### 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: Symbolic Moment Analysis of the Hirsch Citation Index (formerly Size of Durfee Square)

Speaker: ** Doron Zeilberger**, Rutgers University

Date: Thursday, November 13, 2014 5:00pm

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

Abstract:

Once upon a time there was an esoteric and specialized notion, called "size of the Durfee square", of interest to at most 100 specialists
in the whole world. Then it was kissed by a prince called Jorge Hirsch, and became the famous
(and to quite a few people, infamous) h-index, of interest to every scientist, and scholar, since it tells you how productive a scientist (or scholar)
you are! When Rodney Canfield, Sylvie Corteel, and Carla Savage wrote their beautiful 1998 article proving, rigorously,
by a very deep and intricate analysis, the asymptotic normality of the random variable "size of Durfee square" defined
on integer-partitions of n (as n goes to infinity), with precise asymptotics for the mean and variance,
they did not dream that one day their result should be of interest to everyone who has ever published a paper.
However Canfield et. al. had to work really hard to prove their deep result. Here we take an "empirical" shorcut,
that proves the same thing much faster (modulo routine number- and symbol-crunching).
More importantly, the empirical methodology should be useful in many other cases where rigorous proofs are either too hard, or not worth the effort!

(Note: this replaces the originally scheduled talk, by Jonathan Bloom, that had to be postponed. Bloom's talk was
moved to Jan. 29, 2015)

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