History of Science and Engineering Annotation << Back ABOUT COMBINATORIAL RESEARCHES OF G.S. KLGEL A.E. Malykh, A.S. Kalenkova From the last decennials of XVIII century interest in combinatorial researches due to their widespread application in numerous applied disciplines was increased. However at that time the theoretical base of combinatorics significantly was lagged. Scientists of combinatorial school of german mathematicians, whose founder and leader was K.F. Hindenburg, noticed their attention on this fact. Creating of combinatorial theory on a strong foundation was the aim of them. During this time the combinatorial doctrine (combinatorics) and combinatorial analysis were began to considered in isolation. G.S. Klgel was one of leading members of combinatorial school. Analysis of combinatorial materials of dictionary scientist was presented. It was the fi rst mathematical dictionary of that period, in which all combinatorial notions was collected. He was promoted the development of common view on combinatorics. This dictionary was allowed to other scientists in understanding of techniques and approaches to combinatorial facts. The estimation of Klgel contribution in development of doctrine about combinatorial types of compositions and their complexions was given. The historical reference, concerning the binomial and polynomial theorem, and also different types of compositions was given by autor. The defi nition for each of introduced notions was given by him. Numerous algorithms for counting of compositions were developed by scientist. All methods scientist were supported by concrete examples. The information about additive theory of partitions of natural numbers was placed in his work. Autor was presented also treatises of his predecessors and contemporaries in combinatorial analysis and it applications. Some of them were briefl y described by him. Keywords: combinatorics; compositions; complexes of compositions; types; complexes with a given sums; involutions. Contacts: E-mail: malych@pspu.ru Pp. 003-011.