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.

中文翻译：

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计算给定内同态的函数数

提出了一种迭代过程来计算n个变量的k值函数的数量，以使每个变量具有与任何常数和置换都不同的内态。基于此过程，可以找到n个变量的三值函数数量的公式，以使每个变量具有不平凡的内同态。对于任意的半同形半群，可以找到n个变量的所有三值函数集合的幂，以使每个半值具有指定半群的同形。