A Critique of Hirsch’s Citation Index: A Combinatorial Fermi Problem

1.1. Overview. In 2005, physicist J. E. Hirsch [Hi05] proposed the h-index to measure the quality of a researcher’s output. This metric is the largest integer n such that the person has n papers with at least n citations each, and all other papers have weakly less than n citations. Although the original focus of loc. cit. was on physicists, the h-index is now