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arXiv · 2504.07765

Finite pattern problems related to Engel expansion

Chun-Yun Cao·Yang Xiao
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Abstract

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.

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Chun-Yun Cao, Yang Xiao. 2025-04-10. Finite pattern problems related to Engel expansion. https://arxiv.org/abs/2504.07765

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