Non-spherical sets versus lines in Euclidean Ramsey theory
Abstract We show that for every non-spherical set X in $\mathbb {E}^d$ , there exists a natural number m and a red/blue-coloring of $\mathbb {E}^n$ 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.
Authors
- David Conlon (ORCID: https://orcid.org/0000-0001-5899-1829)
- Jakob Führer (ORCID: https://orcid.org/0009-0009-4793-0356)
Institutions
- Johannes Kepler University of Linz (AT)
- California Institute of Technology (US)
Publication Details
- Journal
- Canadian Mathematical Bulletin
- Published
- 2025-08-22
- DOI
- https://doi.org/10.4153/s0008439525101082
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Austrian Science Fund