Kombinatorika dvoičnyh slov i korazmernosti toždestv levonilʹpotentnyh algebr

Zaicev, Mikhail V. (author), Repovš, Dušan (author)

• Language: Russian
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2019
• Number of pages: Str. 35-51
• Numbering: T. 58, vyp. 1
• PID: 20.500.12556/RUL-110555
• UDC: 512.557
• ISSN on article: 0373-9252
• COBISS.SI-ID: 18650201

Note

Angleški prevod v: ZAICEV, M., REPOVŠ, D. Combinatorics on binary words and codimensions of identities in left nilpotent algebras. Algebra and logic, ISSN 0002-5232, Volume 58, Number 1, March 2019, str. 23-35, DOI: 10.1007/s10469-019-09522-6, COBISS.SI-ID 18649945

• Publication date in RUL: 17.09.2019

Record is a part of a journal

• Title: Algebra i logika
• Shortened title: Algebra log.
• Publisher: Institut matematiki im. S.L. Soboleva SO RAN
• ISSN: 0373-9252
• COBISS.SI-ID: 24917248

Secondary language

• Language: English
• Title: Combinatorics on binary words and codimensions of identities in left nilpotent algebras

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. I t is proved that fo r any algebra constructed given a binary word with subexponential function of combinatorial complexity, there exists a Pl-exponent. And its precise value is computed.

• Keywords: left nilpotent algebra, polynomial identity, codimension, subexponential function of combinatorial complexity, PI-exponent