Monotonicity and the Hirsch index
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The Hirsch index is a number that synthesizes a researcher's output. It is the maximum number h such that the researcher has h papers with at least h citations each. Woeginger [Woeginger, G. J. (2008a). An axiomatic characterization of the Hirsch-index. Mathematical Social Sciences, 56(2), 224–232; Woeginger, G. J. (2008b). A symmetry axiom for scientific impact indices. Journal of Informetrics, 2(3), 298–303] characterizes the Hirsch index when indices are assumed to be integer-valued. In this note, the Hirsch index is characterized, when indices are allowed to be real-valued, by adding to Woeginger's monotonicity two axioms in a way related to the concept of monotonicity.
[1] Gerhard J. Woeginger,et al. An axiomatic characterization of the Hirsch-index , 2008, Math. Soc. Sci..
[2] J. E. Hirsch,et al. An index to quantify an individual's scientific research output , 2005, Proc. Natl. Acad. Sci. USA.
[3] Antonio Quesada,et al. More axiomatics for the Hirsch index , 2010, Scientometrics.
[4] Gerhard J. Woeginger,et al. A symmetry axiom for scientific impact indices , 2008, J. Informetrics.