Axiomatizing the Hirsch index: Quantity and quality disjoined

Scientific impact indexes like h are responsive to two parameters: the researcherʹs 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 researcherʹs papers received different numbers of citations or (2) only to axioms that allow for changes in the number of citations received by the researcherʹs papers, but do not require changes in scientific productivity. The axioms used are weak. Specifically, monotonicity is avoided.