Mathematical study of h-index sequences

This paper studies mathematical properties of h-index sequences as developed by Liang [Liang, L. (2006). h-Index sequence and h-index matrix: Constructions and applications. Scientometrics, 69(1), 153–159]. For practical reasons, Liming studies such sequences where the time goes backwards while it is more logical to use the time going forward (real career periods). Both type of h-index sequences are studied here and their interrelations are revealed. We show cases where these sequences are convex, linear and concave. We also show that, when one of the sequences is convex then the other one is concave, showing that the reverse-time sequence, in general, cannot be used to derive similar properties of the (difficult to obtain) forward time sequence. We show that both sequences are the same if and only if the author produces the same number of papers per year. If the author produces an increasing number of papers per year, then Liang’s h-sequences are above the “normal” ones. All these results are also valid for g- and R-sequences. The results are confirmed by the h-, g- and R-sequences (forward and reverse time) of the author.