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