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

Jeffrey Shallit

paper

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

arXiv:2609.05780

Abstract

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

arXiv commentThe results of this paper have now been superseded by the much stronger results in https://arxiv.org/abs/2609.20366

An infinite walk in N16, using only unit steps, with no three collinear points

Abstract

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