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

2014/02/18 by Alexander Yong · 1 voice
Mathematics · #math.HO #math.CO

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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).

Discussions

• Quite cute: a more-or-less combinatorial argument for why h-indices might still be reasonably closely related to raw citation counts, under a simplified model (as well as a few other points of discuss [bsky, 7 points, 0 comments]

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