Published March 2026
| Version Published
Journal Article
Non-spherical sets versus lines in Euclidean Ramsey theory
Creators
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1.
California Institute of Technology
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2.
Johannes Kepler University of Linz
Abstract
We show that for every non-spherical set X in E^d, there exists a natural number m and a red/blue-coloring of E^n for every n such that there is no red copy of X and no blue progression of length m with each consecutive point at distance 1. This verifies a conjecture of Wu and the first author.
Copyright and License
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society.
Acknowledgement
The authors thank Manuel Hauke for helpful conversations regarding equidistribution.
Funding
D.C. was supported by NSF Awards DMS-2054452 and DMS-2348859. J.F. was supported by the Austrian Science Fund (FWF) under the project W1230.
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2406.07718 (arXiv)
Funding
- National Science Foundation
- DMS-2054452
- National Science Foundation
- DMS-2348859
- FWF Austrian Science Fund
- W1230
Dates
- Submitted
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2024-06-11
- Accepted
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2025-08-11
- Available
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2025-08-22Published online
Caltech Custom Metadata
- Caltech groups
- Division of Physics, Mathematics and Astronomy (PMA) , Mathematics Department
- Publication Status
- Published