Geodesic
Combinatorics on binary words and codimensions of identities in left nilpotent algebras
Algebra i logika, Tome 58 (2019) no. 1, pp. 35-51

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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. 
@article{AL_2019_58_1_a2,
     author = {M. V. Zaicev and D. D. Repov\v{s}},
     title = {Combinatorics on binary words and codimensions of identities in left nilpotent algebras},
     journal = {Algebra i logika},
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     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_1_a2/}
}
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M. V. Zaicev; D. D. Repovš. Combinatorics on binary words and codimensions of identities in left nilpotent algebras. Algebra i logika, Tome 58 (2019) no. 1, pp. 35-51. http://geodesic.mathdoc.fr/item/AL_2019_58_1_a2/