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Ralf Stephan

Publications and source records attributed to Ralf Stephan.

7 recordsLinked to original sources
arXiv2026

Aperiodicity and subword complexity in the binary expansion of powers of three

We prove two results on the fine structure of the binary digits of $3^{m}$. First, for every fixed period $p$, the number of positions at which the binary expansion of $3^{m}$ breaks $p$-periodicity grows in order like $\log m/\log\log m$; equivalently, no window of the expansion deeper than a fixed power of $\log m$ is $p$-periodic. Second, the finite binary word formed by the low-order digits of $3^{m}$ has full low-order subword complexity: its complexity function satisfies $p_{3^{m}}(n)\ge n+1$ for every length $n$, once $m$ is large enough.

math.CO↗
arXiv2026

Superlinear complexity of the $(3/2)^n$ steering word

Write $(3/2)^n = m_n + \varepsilon_n$ with $m_n$ the nearest integer and $\varepsilon_n\in[-\tfrac12,\tfrac12)$, and let $T=(t_n)$, $t_n=2m_{n+1}-3m_n$, be the resulting \emph{steering word}: the step-by-step record of the map $x\mapsto\tfrac32 x$ on the orbit of 1, coded by nearest-integer rounding. Using results by Corvaja--Zannier and Nair--Kumar--Rout we prove that the subword complexity $p_{T}(k)$ of $T$ is superlinear, $p_{T}(k)/k\to\infty$. The argument is completely formalized in Lean~4 and rests on a single external input, the Evertse--Schlickewei $S$-arithmetic subspace theorem, from which both cited results are themselves derived within the formalization.

math.NT↗
arXiv2024

Interleaved snowballing: Reducing the workload of literature curators

We formally define the literature (reference) snowballing method and present a refined version of it. We show that the improved algorithm can substantially reduce curator work, even before application of text classification, by reducing the number of candidates to classify. We also present a desktop application named LitBall that implements this and other literature collection methods, through access to the Semantic Scholar academic graph (S2AG).

cs.DL↗
arXiv2007

Lineare Rekurrenzen, Potenzreihen und ihre erzeugenden Funktionen

Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear recurrences tries to fill a gap in the literature by giving many extensive examples.

math.HO↗
arXiv2003

Divide-and-conquer generating functions. Part I. Elementary sequences

Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By giving several classes of ordinary generating functions together with recurrences, we hope to help with the analysis of many such sequences, and try to classify a part of the divide-and-conquer sequence zoo.

math.CO↗