Critique of Hirsch's citation index: a combinatorial Fermi problem

TL;DR

This paper critically examines the h-index by applying combinatorial mathematics and asymptotic analysis to estimate its value from citation counts, providing confidence intervals and a practical rule of thumb.

Contribution

It introduces a novel combinatorial approach to estimate the h-index, including confidence intervals and a simple rule of thumb based on asymptotic theorems.

Findings

Derived confidence intervals for h-index estimates

Proposed a rule of thumb: h ≈ 0.54 × (citations)^{1/2}

Validated the approach with empirical data from mathematicians

Abstract

The h-index was introduced by the physicist J.E. Hirsch in 2005 as measure of a researcher's productivity. We consider the "combinatorial Fermi problem" of estimating h given the citation count. Using the Euler-Gauss identity for integer partitions, we compute confidence intervals. An asymptotic theorem about Durfee squares, due to E.R. Canfield-S. Corteel-C.D. Savage from 1998, is reinterpreted as the rule of thumb h=0.54 x (citations)^{1/2}. We compare these intervals and the rule of thumb to empirical data (primarily using mathematicians).