Method of the Multidimensional Sieve in the Practical Realization of some Combinatorial Algorithms

Abstract: Some difficulties regarding the application of the well-known sieve method are considered in the case when a practical (program) realization of selecting elements, having a particular property among the elements of a set with a sufficiently great cardinal number(cardinality). In this paper the problem has been resolved by using a modified version of the method, utilizing multidimensional arrays. As a theoretical illustration of the method of the multidimensional sieve, the problem of obtaining a single representative of each equivalence class with respect to a given relation of equivalence and obtaining the cardinality of the respective factor set is considered with relevant mathematical proofs.