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Abstract

Fractional counting of authors of multi-authored papers has been shown to lead to a breakdown of Lotka's Law despite its robust character under most circumstances. Kretschmer and Rousseau use the normal count method of full credit for each author on two five-year bibliographies from each of 13 Dutch physics institutes where high co-authorship is a common occurrence. Kolmogorov-Smirnov tests were preformed to see if the Lotka distribution fit the data. All bibliographies up to 40 authors fit acceptably; no bibliography with a paper with over 100 authors fits the distribution. The underlying traditional "success breeds success" mechanism assumes new items on a one by one basis, but Egghe's generalized model would still account for the process. It seems unlikely that Lotka's Law will hold in a high co-authorship environment.

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Abstract

In single-authored bibliographies only single scientist distribution can be found. But in multi-authored bibliographies single scientists distribution, pairs distribution, triples distribution, etc., can be presented. Whereas regarding Lotka's law single scientists P distribution (both in single-authored and in multi-authored bibliographies) is of interest, in the future pairs P, Q distribution, triples P, Q, R distribution, etc. should be considered Starting with pair distribution, the following question arises in the present paper: Is there also any regularity or well-ordered structure for the distribution of coauthor pairs in journals in analogy to Lotka's law for the distribution of single authors? Usually, in information science "laws " or "regularities " (for example Lotka's law) are mathematical descriptions of observed data inform of functions; however explanations of these phenomena are mostly missing. By contrast, in this paper the derivation of a formula for describing the distribution of the number of co-author pairs will be presented based on wellknown regularities in socio psychology or sociology in conjunction with the Gestalt theory as explanation for well-ordered collaboration structures and production of scientific literature, as well as derivations from Lotka's law. The assumed regularities for the distribution of co-author pairs in journals could be shown in the co-authorship data (1980-1998) of the journals Science, Nature, Proc Nat Acad Sci USA and Phys Rev B Condensed Matter.

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Abstract

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. A simple mathematical function is developed for the description of these gestalts which can encompass complementary tendencies (as in the principle of Yin and Yang) in their dynamic interplay and, thus, can reflect the change in gestalts. For example, "Birds of a feather flock together" and "Opposites attract" are explained as complementary tendencies. The data are obtained by SCI. In analyzing the coauthorship networks, coauthorship relations Z between scientists (third dimension) are recorded from the point of view of every scientist with productivity X (first dimension) to all the other scientists with productivity Y (second dimension). According to the conciseness principle, three-dimensional well-ordered gestalts from different science disciplines are presented. The results of the study have confirmed Metzger's conjectures that the conciseness principle also has validity for social systems, and is valid even with the same conciseness as in the psychology of perception. It is possible that the presented mathematical function has assumed a more general character and, in consequence, is also more likely applicable to the description of citation networks or the spreading of information.