Dingding Yu

collaborators

3 papers

math.MG2026

On the maximal run-length function in the Lüroth expansion

Dingding Yu

Let $ \ell_n(x) $ denote the maximal run-length among the first $ n $ digits of the Lüroth expansion of $ x\in(0,1] $. While $ \ell_n(x) $ grows logarithmically, we investi…

math.NT2024

Common substring with shifts in b-ary expansions

Xin Liao, Dingding Yu

Denote by $S_{n} (x, y)$ the length of the longest common substring of $x$ and $y$ with shifts in their first $n$ digits of $b$ -ary expansions. We show that the sets of pairs $(x, y)$ ,…

math.NT2024

Metrical theory of power-2-decaying Gauss-like expansion

Zhihui Li, Xin Liao, Dingding Yu

Each $x \in (0, 1]$ can be uniquely expanded as a power-2-decaying Gauss-like expansion, in the form of \begin{equation*} x=\sum_{i=1}^{\infty}2^{-(d_1(x)+d_2(x)+\cdots+d_i(x))},\qqu…