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The most frequently used indicators for the productivity and impact ofscientists are the total number of publication ($N_{pub}$), total number ofcitations ($N_{cit}$) and the Hirsch (h) index. Since the seminal paper ofHirsch, in 2005, it is largely debated whether the h index can be considered asan indicator independent of $N_{pub}$ and $N_{cit}$. Exploiting the Paretianform for the distribution of citations for the papers authored by a researcher,here we discuss scaling relations between h, $N_{pub}$ and $N_{cit}$. Theanalysis incorporates the Gini index as an inequality measure of citationdistributions and a recently proposed inequality kernel, gintropy (resemblingto the entropy kernel). We find a new upper bound for the h value as a functionof the total number of citations, confimed on massive data collected fromGoogle Scholar. Our analyses reveals also that the individualized Gini indexcalculated for the citations received by the publications of an author peaksaround 0.8, a value much higher than the one characteristic for the usualsocio-economic inequalities.

Gintropic Scaling of Scientometric Indexes