Title 



A mathematical characterization of the Hirschindex by means of minimal increments


Author 


 

Abstract 



The minimum configuration to have a hindex equal to h is h papers each having h citations, hence h(2) citations in total. To increase the hindex to h + 1 we minimally need (h + 1)(2) citations, an increment of I1(h) = 2h + 1. The latter number increases with 2 per unit increase of h. This increment of the second order is denoted I2(h) =2. If we define I1 and I2 for a general Hirsch configuration (say n papers each having f(n) citations) we calculate I1(f) and I2(f) similarly as for the hindex. We characterize all functions f for which I2(f) = 2 and show that this can be obtained for functions f(n) different from the hindex. We show that f(n) = n (i.e. the hindex) if and only if I2(f) = 2, f(1) = 1 and f(2) = 2. We give a similar characterization for the threshold index (where n papers have a constant number C of citations). Here we deal with second order increments I2(f) = 0. (c) 2013 Elsevier Ltd. All rights reserved.  

Language 



English


Source (journal) 



Journal of informetrics.  Amsterdam 

Publication 



Amsterdam : 2013


ISSN 



17511577


Volume/pages 



7:2(2013), p. 388393


ISI 



000318377100016


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Full text (publishers version  intranet only) 


 
