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Algebra i logika, 2019, Volume 58, Number 1, Pages 35–51
DOI: https://doi.org/10.33048/alglog.2019.58.103 (Mi al880) 		 
Combinatorics on binary words and codimensions of identities in left nilpotent algebras

M. V. Zaiceva, D. D. Repovšb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Univerza v Ljubljani, Kongresni trg 12, 1000 Ljubljana, SLOVENIA
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DOI: https://doi.org/10.33048/alglog.2019.58.103
Abstract: 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.
Keywords: left nilpotent algebra, polynomial identity, codimension, subexponential function of combinatorial complexity, PI-exponent.
Funding agency Grant number
Russian Science Foundation 16-11-10013
Slovenian Research Agency BI-RU/16-18-002
P1-0292
J1-8131
J1-7025
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.
Received: 25.09.2017
Revised: 07.05.2019
English version:
Algebra and Logic, 2019, Volume 58, Issue 1, Pages 23–35
DOI: https://doi.org/10.1007/s10469-019-09522-6
Bibliographic databases:
Document Type: Article
UDC: 512.57
Language: Russian
Citation: M. V. Zaicev, D. D. Repovš, “Combinatorics on binary words and codimensions of identities in left nilpotent algebras”, Algebra Logika, 58:1 (2019), 35–51; Algebra and Logic, 58:1 (2019), 23–35
Citation in format AMSBIB
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\paper Combinatorics on binary words and codimensions of identities in left nilpotent algebras
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\issue 1
\pages 35--51
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