Estimating the number of variants in the solution of a certain class of problem

Abstract

The development of mathemat ics and the vigorous growth of computational techniques has led to the widespread application of this science, and to a growing role of finite mathematics , especial ly of such an important domain as combinatorial analysis. Recently, it has become necessa ry to solve a large number of problems of the graph construct ion type, scheduling, and the design and automatization of production p r o c e s ses which reduce to combinatorial problems. In solving each problem, all the possible var iants must be studied separately. The est imate of each variant is usually connected with a large volume of computation, and thus it is often necessa ry to know exactly the number of var iants satisfying the conditions of the problem. The known methods of combinatorial analysis make it possible to get only a very excessive est imate. We now propose a method for finding an exact es t imate for a cer ta in c lass of problem.