Which Index?

Algebra Level 3

It is often difficult to compare the 'worth' of the research work done by two researchers. One way to quantify this is to use the number of citations. Currently, there are two indices which are used for this purpose.

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

g-index : Given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the (unique) largest number such that the top g g articles received (together) at least g 2 g^2 citations.

An author with N p N_p publications has a h-index of n h n_h and a g-index of n g n_g . Which of these statements is always true?

( n g 2 − n h 2 ) 2 4 ≤ n h \sqrt[4]{\left(n_g^2-n_h^2\right)^{2}} \le n_h None of the rest n h ≤ n g n_h \le n_g n h ≥ n g n_h \ge n_g

Janardhanan Sivaramakrishnan by Janardhanan Sivaramakris… , 42

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1 solution

Let the h index be n h n_h .

Let the number of first n h n_h papers be

c 1 ≥ c 2 ≥ c 3 ≥ ⋯ ≥ c n h ≥ n h c_1 \ge c_2 \ge c_3 \ge \cdots \ge c_{n_h} \ge n_h and c n h + 1 < n h + 1 c_{n_h+1} < n_h+1

This means that ∑ i = 1 n h c i ≥ n h 2 \sum_{i=1}^{n_h} c_i \ge n_h^2

Thus, the total number of citations for the first n h n_h papers would at least be equal to n h 2 n_h^2 .

Thus, n h ≤ n g n_h \le n_g

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