Relative position in binary substitutions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912073849503744 |
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| author | Coons, Michael Ramsey, Christopher Strungaru, Nicolae |
| author_facet | Coons, Michael Ramsey, Christopher Strungaru, Nicolae |
| contents | Given an infinite word ${\bf w}$ on a finite alphabet, an immediate question arises:~can we understand the frequency of letters in ${\bf w}$\,? For words that are the fixed points of substitutions, the answer to this question is often `yes' -- the details and methods of these answers have been well-documented. In this paper, toward a better-understanding of the fixed points of binary substitutions, we delve deeper by investigating, in fine detail, the position of letters by defining various position functions and proving results about their behavior. Our analysis reveals new information about the Fibonacci substitution and the extended Pisa family of substitutions, as well as a new characterization of the Thue--Morse sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative position in binary substitutions Coons, Michael Ramsey, Christopher Strungaru, Nicolae Combinatorics Discrete Mathematics 05A05, 68R15, 11B05 Given an infinite word ${\bf w}$ on a finite alphabet, an immediate question arises:~can we understand the frequency of letters in ${\bf w}$\,? For words that are the fixed points of substitutions, the answer to this question is often `yes' -- the details and methods of these answers have been well-documented. In this paper, toward a better-understanding of the fixed points of binary substitutions, we delve deeper by investigating, in fine detail, the position of letters by defining various position functions and proving results about their behavior. Our analysis reveals new information about the Fibonacci substitution and the extended Pisa family of substitutions, as well as a new characterization of the Thue--Morse sequence. |
| title | Relative position in binary substitutions |
| topic | Combinatorics Discrete Mathematics 05A05, 68R15, 11B05 |
| url | https://arxiv.org/abs/2410.12173 |