Article
| Title: | Finite pattern problems related to Engel expansion (English) |
| Author: | Cao, Chun-Yun |
| Author: | Xiao, Yang |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 177-190 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $\mathcal {F}$ be a countable collection of functions $f$ defined on 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 every finite pattern of $\mathcal {F}$, with applications demonstrated through representative examples. (English) |
| Keyword: | Engel expansion |
| Keyword: | finite pattern |
| Keyword: | upper Banach density |
| Keyword: | arithmetic progression |
| Keyword: | geometric progression |
| MSC: | 11K55 |
| MSC: | 28A80 |
| DOI: | 10.21136/CMJ.2026.0212-25 |
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| Date available: | 2026-03-13T09:31:41Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153567 |
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