PreprintCC BY 4.0arXiv
An infinite walk in ℕ16, using only unit steps, with no three collinear points
Abstract
Is it possible to walk to infinity, avoiding three collinear points, using as steps only the standard unit basis vectors (0,0,…, 0, 1, 0, …, 0)? We prove this is possible in $16$ dimensions.
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BibTeX
@misc{shallit2026infinite,
title = {{An infinite walk in $\mathbbN^16$, using only unit steps, with no three collinear points}},
author = {Jeffrey Shallit},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05780},
eprint = {2609.05780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05780},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An infinite walk in ℕ^16, using only unit steps, with no three collinear points
AU - Jeffrey Shallit
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.05780
UR - https://arxiv.org/abs/2609.05780
AB - Is it possible to walk to infinity, avoiding three collinear points, using as steps only the standard unit basis vectors (0,0,…, 0, 1, 0, …, 0)? We prove this is possible in $16$ dimensions.
ER -