Title
A new short proof of Naranan's theorem, explaining Lotka's law and Zipf's law A new short proof of Naranan's theorem, explaining Lotka's law and Zipf's law
Author
Faculty/Department
Faculty of Social Sciences. Instructional and Educational Sciences
Publication type
article
Publication
Washington, D.C. ,
Subject
Documentation and information
Source (journal)
Journal of the American Society for Information Science. - Washington, D.C., 1970 - 2000
Volume/pages
61(2010) :12 , p. 2581-2583
ISSN
0002-8231
ISI
000284231100016
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
Naranan's important theorem, published in Nature in 1970, states that if the number of journals grows exponentially and if the number of articles in each journal grows exponentially (at the same rate for each journal), then the system satisfies Lotka's law and a formula for the Lotka's exponent is given in function of the growth rates of the journals and the articles. This brief communication re-proves this result by showing that the system satisfies Zipf's law, which is equivalent with Lotka's law. The proof is short and algebraic and does not use infinitesimal arguments.
E-info
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