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Informational Complexity of the Generating Subset of Crystallographic Groups

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Abstract

By analogy with the Shannon’s complexity of graphs, the complexity of minimal generating subsets of finitely generated discrete groups, including crystallographic ones, was introduced. The introduced value can be useful in the analysis of molecular structures and other ones with fuzzy bearing contacts. An algorithm was developed, and the calculation results are presented for some finite groups, including crystal classes.

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Funding

This study was supported by the Russian Science Foundation (project no. 20-77-10065). The calculation of informational indices, performed by D.A. Banaru, was supported by State contract no. 0137-2019-0014.

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Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    A. M. Banaru

  2. Kola Science Centre, Russian Academy of Sciences, 184209, Apatity, Russia

    A. M. Banaru & S. M. Aksenov

  3. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, 119334, Moscow, Russia

    D. A. Banaru

Authors
  1. A. M. Banaru
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  2. D. A. Banaru
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  3. S. M. Aksenov
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Correspondence to A. M. Banaru or S. M. Aksenov.

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Translated by Yu. Sin’kov

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Banaru, A.M., Banaru, D.A. & Aksenov, S.M. Informational Complexity of the Generating Subset of Crystallographic Groups. Crystallogr. Rep. 67, 521–529 (2022). https://doi.org/10.1134/S106377452203004X

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  • DOI: https://doi.org/10.1134/S106377452203004X

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