The Hirsch-index of set partitions

The Hirsch-index (h-index) is calculated on citations that papers (e. g. of authors or journals) receive. Hence we can consider the h-index as calculated on a partition of the same set of citations. In this paper we will study the h-index, dependent on the particular partition of this set. We will do this in the discrete case as well as in a continuous Lotkaian setting. In the discrete setting we will determine h-indices of successive refinements of partitions. We show that the corresponding h-indices do not form a monotonic sequence and we determine the maximal value of an h-index in such a system. In the continuous Lotkaian setting we prove that, given a set of citations of cardinality A, the h-index only depends on the average number of citations that an author or a journal receives. This functional dependence is calculated and we show that it has a unique maximum for which formulae are given. This is the highest possible h-index, given a set of citations of fixed cardinality. Examples confirm the theory.