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A New Formulation of a Criterion for the Minimal Logarithmic Growth Rate

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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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119234, Moscow, Russia

    S. A. Komkov

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  1. S. A. Komkov
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Correspondence to S. A. Komkov.

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The authors declare that they have no conflicts of interest.

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Translated by I. Tselishcheva

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Komkov, S.A. A New Formulation of a Criterion for the Minimal Logarithmic Growth Rate. Moscow Univ. Math. Bull. 75, 220–221 (2020). https://doi.org/10.3103/S0027132220050046

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  • DOI: https://doi.org/10.3103/S0027132220050046

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