More axiomatics for the Hirsch index

The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the monotonicity axiom.