Abstract

We obtain a new formulation of a criterion for the minimal logarithmic growth rate for an arbitrary finite set with a given set of operations. It turns out that a finite set with operations has the minimal logarithmic growth rate if and only if the set of operations is not entirely contained in any of the precomplete (maximal) classes other than the classes preserving subsets and the classes of functions that preserve predicates given by permutations decomposable into cycles of the same prime length.

中文翻译：

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最小对数增长率准则的新公式

摘要

我们为具有给定操作集的任意有限集获得了最小对数增长率的准则的新公式。事实证明，当且仅当操作集不完全包含在任何保留子集（最大）类中（保留子集的类和保留谓词的函数的类除外）时，带有操作的有限集的对数增长率最小由可分解为相同素数长度的周期的排列给出。