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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Original Russian Text © S.S. Marchenkov, A.V. Chernyshev, 2018, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’nayaMatematika i Kibernetika, 2018, No. 4, pp. 26–31.
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Marchenkov, S.S., Chernyshev, A.V. Calculating the Number of Functions with a Given Endomorphism. MoscowUniv.Comput.Math.Cybern. 42, 171–176 (2018). https://doi.org/10.3103/S0278641918040052
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DOI: https://doi.org/10.3103/S0278641918040052