Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 27 min ago
PreprintCC BY 4.0arXiv

An infinite small-step ℤ3-walk with no collinear triple

  • Stijn Cambie
  • Erik Kalviainen
Open at sourcePDFDOICite

Abstract

We construct an infinite walk in ℤ3 whose steps come from a fixed set of sixteen vectors and no three of whose vertices are collinear, answering a problem of Gerver and Ramsey popularized as Erdős Problem 193.

Related

  1. An infinite walk in ℕ16, using only unit steps, with no three collinear points
    Jeffrey Shallit
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. Biased random walk on a locally infinite Galton-Watson tree
    Jan Nagel
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  3. Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes
    Xiequan Fan, Shuyuan Liang, Dongxue Ma
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Normal approximation, moderate and large deviations for the elephant random walk with stops and random step sizes
    Shuyuan Liang
    arXivPreprintCC BY-NC-ND 4.0Full textProbabilityarXiv
  5. Amnesic Elephant Random Walk with Polynomially Decaying Step Sizes
    Shyan Ghosh, Manisha Dhillon, Kuldeep Kumar Kataria
    arXivPreprintarXiv licenceFull textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{cambie2026infinite,
  title = {{An infinite small-step $\mathbb Z^3$-walk with no collinear triple}},
  author = {Stijn Cambie and Erik Kalviainen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01766},
  eprint = {2609.01766},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01766},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An infinite small-step ℤ^3-walk with no collinear triple
AU  - Stijn Cambie
AU  - Erik Kalviainen
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01766
UR  - https://arxiv.org/abs/2609.01766
AB  - We construct an infinite walk in ℤ^3 whose steps come from a fixed set of sixteen vectors and no three of whose vertices are collinear, answering a problem of Gerver and Ramsey popularized as Erdős Problem 193.
ER  -