2-balanced sequences coding rectangle exchange transformation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913272237654016 |
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| author | Dvořáková, Lubomíra Masáková, Zuzana Pelantová, Edita |
| author_facet | Dvořáková, Lubomíra Masáková, Zuzana Pelantová, Edita |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2-balanced sequences coding rectangle exchange transformation Dvořáková, Lubomíra Masáková, Zuzana Pelantová, Edita Combinatorics 68R15 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. |
| title | 2-balanced sequences coding rectangle exchange transformation |
| topic | Combinatorics 68R15 |
| url | https://arxiv.org/abs/2403.12791 |