Special features of the author-publication relationship and a new explantation of Lotkas law based on convolution theory

Abstract

This article makes the obvious but rather unexploited remark that there is a structural difference between author-publication systems and, for example, journal-article systems, in the sense that articles are published in one journal but that papers can have several authors. This difference is then studied mathematically, using convolutions in order to derive the several-author case from the case of a single author per paper. We show that Lotka's law phi(i) = CI(i + 1)alpha, where i greater-than-or-equal-to 0 is approximately stable for all alpha = 2, 3, 4,..., meaning that if Lotka's law is valid in systems in which every article has one author then it is approximately valid (in a mathematically strong sense) (with the same alpha) in the general systems, where more than one author per paper is possible. We also show that the same is true (but in an exact way) for the geometric distribution. Hence, this theory provides intrinsic explanations of the Lotka and geometric functions.