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Some difficulties regarding the application of the well-known sieve methodare considered in the case when a practical (program) realization of selectingelements, having a particular property among the elements of a set with asufficiently great cardinal number(cardinality). In this paper the problem hasbeen resolved by using a modified version of the method, utilizingmultidimensional arrays. As a theoretical illustration of the method of themultidimensional sieve, the problem of obtaining a single representative ofeach equivalence class with respect to a given relation of equivalence andobtaining the cardinality of the respective factor set is considered withrelevant mathematical proofs.

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