Ternary is Still Good for Parikh Matrices
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916445926981632 |
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| author | Mercaş, Robert Teh, Wen Chean |
| author_facet | Mercaş, Robert Teh, Wen Chean |
| contents | The focus of this work is the study of Parikh matrices with emphasis on two concrete problems. In the first part of our presentation we show that a conjecture by Dick at al. in 2021 only stands in the case of ternary alphabets, while providing counterexamples for larger alphabets. In particular, we show that the only type of distinguishability in the case of 3-letter alphabets is the trivial one. The second part of the paper builds on the notion of Parikh matrices for projections of words, discussed initially in this work, and answers, once more in the case of a ternary alphabet, a question posed by Atanasiu et al. in 2022 with regards to the minimal Hamming distance in between words sharing a congruency class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ternary is Still Good for Parikh Matrices Mercaş, Robert Teh, Wen Chean Combinatorics 68R15, 05A05 The focus of this work is the study of Parikh matrices with emphasis on two concrete problems. In the first part of our presentation we show that a conjecture by Dick at al. in 2021 only stands in the case of ternary alphabets, while providing counterexamples for larger alphabets. In particular, we show that the only type of distinguishability in the case of 3-letter alphabets is the trivial one. The second part of the paper builds on the notion of Parikh matrices for projections of words, discussed initially in this work, and answers, once more in the case of a ternary alphabet, a question posed by Atanasiu et al. in 2022 with regards to the minimal Hamming distance in between words sharing a congruency class. |
| title | Ternary is Still Good for Parikh Matrices |
| topic | Combinatorics 68R15, 05A05 |
| url | https://arxiv.org/abs/2410.15004 |