Stefan Steinerberger

activity

20242026

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5 papers · 1 filter

math.CO2025

Balanced Stick Breaking

FranÃ§ois ClÃ©ment, Stefan Steinerberger

Consider an infinite sequence $(x_{k})_{k = 1}^{\infty}$ on the unit circle $S^{1}$ . We may interpret the first $n$ elements $(x_{k})_{k = 1}^{n}$ as places where the `circular stic…

math.CO2025

Many antipodes implies many neighbors

Stefan Steinerberger

Suppose ${x_{1}, \dots, x_{n}} \subset R^{2}$ is a set of $n$ points in the plane with diameter $\leq 1$ , meaning $∥ x_{i} - x_{j} ∥ \leq 1$ for all $1 \leq i, j \leq n$ …

math.CO2025

Small gaps in the Ulam sequence

FranÃ§ois ClÃ©ment, Stefan Steinerberger

The Ulam sequence, described by Stanislaw Ulam in the 1960s, starts $1, 2$ and then iteratively adds the smallest integer that can be uniquely written as the sum of two distinct ear…

math.CO2024

On differences of two harmonic numbers

Jeck Lim, Stefan Steinerberger

We prove that the existence of infinitely many $(m_{k}, n_{k}) \in N^{2}$ such that the difference of harmonic numbers $H_{m_{k}} - H_{n_{k}}$ approximates 1 well $$ \lim_{k \righta…

math.CO2024

On a problem involving unit fractions

Stefan Steinerberger

ErdÅs and Graham proposed to determine the number of subsets $S \subseteq {1, 2, \dots, n}$ with $\sum_{s \in S} 1/ s = 1$ and asked, among other things, whether that num…