2014/10/31 by Shalosh B. Ekhad, Doron Zeilberger, Ekhad, Shalosh B. +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.1411.0002
openalex publication_date 2014/10/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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" shortcut, 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 trouble!