Investigations on the step-based research indices of Chambers and Miller

In a recent paper, Chambers and Miller introduced two fundamental axioms for scientific research indices. We perform a detailed analysis of these two axioms, thereby providing clean combinatorial characterizations of the research indices that satisfy these axioms and of the so-called step-based indices. We single out the staircase indices as a particularly simple subfamily of the step-based indices, and we provide a simple axiomatic characterization for them.