A note on symmetries of rich sequences with minimum critical exponent
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916584136638464 |
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| author | Dvořáková, Lubomíra Pelantová, Edita |
| author_facet | Dvořáková, Lubomíra Pelantová, Edita |
| contents | Using three examples of sequences over a finite alphabet, we want to draw attention to the fact that these sequences having the minimum critical exponent in a given class of sequences show a large degree of symmetry, i.e., they are G-rich with respect to a group G generated by more than one antimorphism. The notion of G-richness generalizes the notion of richness in palindromes which is based on one antimorphism, namely the reversal mapping. The three examples are: 1) the Thue-Morse sequence which has the minimum critical exponent among all binary sequences; 2) the sequence which has the minimum critical exponent among all binary rich sequences; 3) the sequence which has the minimum critical exponent among all ternary rich sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on symmetries of rich sequences with minimum critical exponent Dvořáková, Lubomíra Pelantová, Edita Combinatorics 68R15 Using three examples of sequences over a finite alphabet, we want to draw attention to the fact that these sequences having the minimum critical exponent in a given class of sequences show a large degree of symmetry, i.e., they are G-rich with respect to a group G generated by more than one antimorphism. The notion of G-richness generalizes the notion of richness in palindromes which is based on one antimorphism, namely the reversal mapping. The three examples are: 1) the Thue-Morse sequence which has the minimum critical exponent among all binary sequences; 2) the sequence which has the minimum critical exponent among all binary rich sequences; 3) the sequence which has the minimum critical exponent among all ternary rich sequences. |
| title | A note on symmetries of rich sequences with minimum critical exponent |
| topic | Combinatorics 68R15 |
| url | https://arxiv.org/abs/2501.15135 |