The Ramsey-to-canonical Ramsey conjecture for configurations
The Ramsey-to-canonical Ramsey conjecture for configurations
Let be a configuration. It is Ramsey if for every there exists a dimension such that . A configuration exhibits the canonical Ramsey property if, for every and all sufficiently large dimensions, every -coloring of the ambient Euclidean space contains a monochromatic or rainbow congruent copy of . Ramsey-to-canonical Ramsey conjecture. If is Ramsey, then exhibits the canonical Ramsey property. This would unify the known canonical Ramsey results for rectangles, triangles, and certain simplices; determining whether all simplices have the canonical Ramsey property remains open.
Sources & referencesView supporting material
Primary source
Yijia Fang, Gennian Ge, Yang Shu, Qian Xu, Zixiang Xu and Dilong Yang, “Canonical Ramsey: triangles, rectangles and beyond”, arXiv:2510.11638 (2025).
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