An infinite walk in $\mathbb{N}^{16}$ , using only unit steps, with no three collinear points

Jeffrey Shallit

Source record

Source: arXiv

Published: Sep 5, 2026

arXiv: 2609.05780

Open original source ↗

Source abstract

Is it possible to walk to infinity, avoiding three collinear points, using as steps only the standard unit basis vectors $(0,0,\ldots, 0, 1, 0, \ldots, 0)$ ? We prove this is possible in $16$ dimensions.

Evidence graph

No public relationships recorded yet.

Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.

An infinite walk in $\mathbb{N}^{16}$, using only unit steps, with no three collinear points — Mathematical Frontier Network