Abstract

An iterative procedure is proposed for calculating the number of k-valued functions of n variables such that each one has an endomorphism different from any constant and permutation. Based on this procedure, formulas are found for the number of three-valued functions of n variables such that each one has nontrivial endomorphisms. For any arbitrary semigroup of endomorphisms, the power is found of the set of all three-valued functions of n variables such that each one has endomorphisms from a specified semigroup.

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