# construct for h-index and Eddington number

There is a construct very useful to measure the efficiency taking into account both quantity and quality, which states something like

N is the highest number that fulfils the statement "in this set, there are at least N elements having at least size/quality/goodness N".

This construct is the basis of the h-index (2005),

A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np − h) papers have no more than h citations each.

But had been previously used by Arthur Eddington to value a cyclist's performance with his Eddington number (before 1944):

the maximum number E such that the cyclist has cycled E miles on E days

This resembles also the Pareto principle (1896), when he first stated that:

approximately 80% of the land in Italy was owned by 20% of the population

Which is a sort of "inverted" version of the "h-index/Eddington number" construct (however, Pareto's principle, using that formulation, does not use the original construct).

So the question is:

Is there an earlier use of the h-index/Eddington number construct? Is this construct known with a more general name, or a more general definition?

## 1 Answer

A Durfee square can be defined for every integer partition. It was introduced before 1883 (which makes it anterior to Pareto's work). It is the construct at the root of both Eddigton number and h-index.

Example of a Durfee square :

x x x * * * *
x x x * *
x x x *
* * *
*


Here the Durfee square of the set {1,3,4,5,7} is the 3x3 square highlighted as there are not 4 elements greater than 4 in the set.

• Superb! This is what I was looking for! – Eynar Oxartum Apr 24 '15 at 13:13