On the h-index, the size of the Hirsch core and Jin's A-index

Hirsch's h-index seeks to give a single number that in some sense summarizes an author's research output and its impact. Essentially, the h-index seeks to identify the most productive core of an author's output in terms of most received citations. This most productive set we refer to as the Hirsch core, or h-core. Jin's A-index relates to the average impact, as measured by the average number of citations, of this “most productive” core. In this paper, we investigate both the total productivity of the Hirsch core – what we term the size of the h-core – and the A-index using a previously proposed stochastic model for the publication/citation process, emphasising the importance of the dynamic, or time-dependent, nature of these measures. We also look at the inter-relationships between these measures. Numerical investigations suggest that the A-index is a linear function of time and of the h-index, while the size of the Hirsch core has an approximate square-law relationship with time, and hence also with the A-index and the h-index.