Axiomatizing the Hirsch index: Quantity and quality disjoined

Scientific impact indexes like h are responsive to two parameters: the researcher's productivity given by the number of her published papers (an aspect of quantity) and citations (an aspect of quality). In this paper I prove that the two parameters can be treated separately: the index h can be axiomatized by appealing (1) only to axioms that allow for productivity changes, but do not require taking into account distinct situations in which a researcher's papers received different numbers of citations or (2) only to axioms that allow for changes in the number of citations received by the researcher's papers, but do not require changes in scientific productivity. The axioms used are weak. Specifically, monotonicity is avoided.

► A scientific impact index usually depends on two parameters (publications and citations).
► It is argued that the two parameters can be disjoined.
► The index h can be axiomatized in terms of axioms that take into account only variations in the publication list.
► The index h can be axiomatized in terms of axioms that take into account only variations in the citation record.