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2-Balanced Sequences Coding Rectangle Exchange Transformation.

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Title: 2-Balanced Sequences Coding Rectangle Exchange Transformation.
Authors: Dvořáková, Lubomíra1 (AUTHOR) lubomira.dvorakova@fjfi.cvut.cz, Masáková, Zuzana1 (AUTHOR) zuzana.masakova@fjfi.cvut.cz, Pelantová, Edita1 (AUTHOR) edita.pelantova@fjfi.cvut.cz
Source: Theory of Computing Systems. Dec2024, Vol. 68 Issue 6, p1537-1555. 19p.
Subjects: Number systems, Rectangles
Abstract: We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any given letter frequencies. We provide an upper bound on factor and abelian complexity of these sequences. Using the interpretation by rectangle exchange transformation, we prove that for almost all triples of letter frequencies, the upper bound on factor and abelian complexity is reached. The bound on factor complexity is given using a number-theoretical function which we compute explicitly for a class of parameters. [ABSTRACT FROM AUTHOR]
Copyright of Theory of Computing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 2-Balanced Sequences Coding Rectangle Exchange Transformation.
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  Data: We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any given letter frequencies. We provide an upper bound on factor and abelian complexity of these sequences. Using the interpretation by rectangle exchange transformation, we prove that for almost all triples of letter frequencies, the upper bound on factor and abelian complexity is reached. The bound on factor complexity is given using a number-theoretical function which we compute explicitly for a class of parameters. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theory of Computing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00224-024-10188-6
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      – TitleFull: 2-Balanced Sequences Coding Rectangle Exchange Transformation.
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              Text: Dec2024
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