History of Science and Engineering Annotation << Back ABOUT COMBINATORIAL RESEARCHES OF H.A. ROTHE A.E. Malykh, A.S. Kalenkova In the last decennials of XVIII century combinatorial methods obtained widespread occurrence due to their application in natural and applied disciplines. However the theoretical base of combinatorics significantly was lagged. At that time views at the combinatorial analysis and its applications were changed. Researches of combinatorial school of german mathematicians, whose founder and leader was K.F. Hindenburg, promoted by this. In it the combinatorial doctrine or combinatorics and combinatorial analysis were separately considered. G.A. Rothe was one of leading members of combinatorial school. Information about life and scientifi c activities of him are provided. He published the results of his researches in memoirs. Analysis some of them was presented. The estimation of him contribution in development of doctrine about combinatorial types of compositions and combinatorial analysis are given. The foundations of permutations and substitutions theory was laid by Rothe. Types of permutations, formulas for their counting were presented, properties were studied, relationships were clarifi ed and applications were showed by him. The historical reference, relating to the theory of series, was given by scientist. The formulas of the inversion of series and functions were proved by Rothe with using combinatorial-analytical method. All formulas were supported by numerous examples. Doctrine about combinatorial integrals was developed; their defi nition was given, properties were presented and application was showed by him. Keywords: combinatorics; theory of permutations and substitutions; combinatorial analysis; series; inversion of series and functions; combinatorial integrals. Contacts: E-mail: malych@pspu.ru Pp. 003-009.