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Infinite sequences and their h-type indices

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  • Egghe, Leo
  • Rousseau, Ronald

Abstract

Starting from the notion of h-type indices for infinite sequences we investigate if these indices satisfy natural inequalities related to the arithmetic, the geometric and the harmonic mean. If f denotes an h-type index, such as the h- or the g-index, then we investigate inequalities such as min(f(X),f(Y)) ≤ f((X + Y)/2) ≤ max(f(X), f(Y)). We further investigate if: f(min(X,Y)) = min(f(X),f(Y)) and if f(max(X,Y)) = max(f(X),f(Y)). It is shown that the h-index satisfies all the equalities and inequalities we investigate but the g-index does not always, while it is always possible to find a counterexample involving the R-index. This shows that the h-index enjoys a number of interesting mathematical properties as an operator in the partially ordered positive cone (R+)∞ of all infinite sequences with non-negative real values.

Suggested Citation

  • Egghe, Leo & Rousseau, Ronald, 2019. "Infinite sequences and their h-type indices," Journal of Informetrics, Elsevier, vol. 13(1), pages 291-298.
    • Handle: RePEc:eee:infome:v:13:y:2019:i:1:p:291-298
    DOI: 10.1016/j.joi.2019.01.005
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    References listed on IDEAS

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    1. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    2. Denis Bouyssou & Thierry Marchant, 2011. "Ranking scientists and departments in a consistent manner," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(9), pages 1761-1769, September.
    3. Vladimir G. Deineko & Gerhard J. Woeginger, 2009. "A new family of scientific impact measures: The generalized Kosmulski-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(3), pages 819-826, September.
    4. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    5. Ronald Rousseau, 2016. "Citation data as a proxy for quality or scientific influence are at best PAC (probably approximately correct)," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 67(12), pages 3092-3094, December.
    6. Egghe, L., 2011. "Characterizations of the generalized Wu- and Kosmulski-indices in Lotkaian systems," Journal of Informetrics, Elsevier, vol. 5(3), pages 439-445.
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    Cited by:

    1. Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    2. Leo Egghe & Ronald Rousseau, 2020. "Minimal Impact One-Dimensional Arrays," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    3. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).

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