Finite pattern problems related to Engel expansion
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908311675207680 |
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| author | Cao, Chun-Yun Xiao, Yang |
| author_facet | Cao, Chun-Yun Xiao, Yang |
| contents | Let $\mathcal{F}$ be a countable collection of functions $f$ defined on the integers with integer values, such that for every $f\in \mathcal{F}$, $f(n)\to +\infty$ as $n\to +\infty$. This paper primarily investigates the Hausdorff dimension of the set of points whose digit sequences of the Engel expansion are strictly increasing and contain any finite pattern of $\mathcal{F}$, demonstrating applications with representative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite pattern problems related to Engel expansion Cao, Chun-Yun Xiao, Yang Number Theory 28A80, 11K55 Let $\mathcal{F}$ be a countable collection of functions $f$ defined on the integers with integer values, such that for every $f\in \mathcal{F}$, $f(n)\to +\infty$ as $n\to +\infty$. This paper primarily investigates the Hausdorff dimension of the set of points whose digit sequences of the Engel expansion are strictly increasing and contain any finite pattern of $\mathcal{F}$, demonstrating applications with representative examples. |
| title | Finite pattern problems related to Engel expansion |
| topic | Number Theory 28A80, 11K55 |
| url | https://arxiv.org/abs/2504.07765 |