Mathematical relations of the h-index with other impact measures in a Lotkaian framework

In a Lotkaian framework there exist formulae for impact measures such as the h-index, g-index, R-index and Randic's H-index. Given two situations in which the h-indices are equal, we establish the functional relation of the R-, g- and H-index of Randic with the total number of papers. In all cases we have a decreasing relationship which can also be explained from a concentration point of view. Variants of relations between these measures are also proved. We also prove a Lotkaian formula for the pi-index of Vinkler. We indicate that the square root of this index is better in line with the other indices and we also show that the previously established results on the h-, g-, R- and H-index are not valid for the pi- or root pi-index. (C) 2010 Elsevier Ltd. All rights reserved.