Conjugate partitions in informetrics: Lorenz curves, h-type indices, Ferrers graphs and Durfee squares in a discrete and continuous setting

Abstract

The well-known discrete theory of conjugate partitions, Ferrers graphs and Durfee squares is interpreted in informetrics. It is shown that partitions and their conjugates have the same h-index, a fact that is not true for the g- and R-index. A modification of Ferrers graph is presented, yielding the g-index. We then present a formula for the Lorenz curve of the conjugate partition in function of the Lorenz curve of the original partition in the discrete setting. Ferrers graphs, Durfee squares and conjugate partitions are then defined in the continuous setting where variables range over intervals. Conjugate partitions are nothing else than the inverses of rank-frequency functions in informetrics. Also here they have the same h-index and we can again give a formula for the Lorenz curve of the conjugate partition in function of the Lorenz curve of the original partition. Calculatory examples are given where these Lorenz curves are equal and where one Lorenz curve dominates the other one. We also prove that the Lorenz curve of a partition and the one of its conjugate can intersect on the open interval 0,1 .