Stefan Steinerberger

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20242026

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math.CO2025

Balanced Stick Breaking

François Clément, 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

François Clément, 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…