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Combinatorics on Binary Words and Codimensions of Identities in Left Nilpotent Algebras

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Algebra and Logic Aims and scope

Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with specified properties of the codimension sequence. However, the class of the infinite words used was confined to periodic words and Sturm words. Here the previously proposed approach is generalized to a considerably more general case. It is proved that for any algebra constructed given a binary word with subexponential function of combinatorial complexity, there exists a PI-exponent. And its precise value is computed.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

    M. V. Zaicev

  2. Univerza v Ljubljani, Kongresni trg 12, 1000, Ljubljana, Slovenia

    D. D. Repovš

Authors
  1. M. V. Zaicev
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  2. D. D. Repovš
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Correspondence to M. V. Zaicev.

Additional information

*Supported by Russian Science Foundation, project 16-11-10013.

**Supported by Slovenian Research Agency, project Nos. BI-RU/16-18-002, P1-0292, J1-8131, and J1-7025.

Translated from Algebra i Logika, Vol. 58, No. 1, pp. 35-51, January-February, 2019.

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Zaicev, M.V., Repovš, D.D. Combinatorics on Binary Words and Codimensions of Identities in Left Nilpotent Algebras. Algebra Logic 58, 23–35 (2019). https://doi.org/10.1007/s10469-019-09522-6

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  • DOI: https://doi.org/10.1007/s10469-019-09522-6

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