A nearcircumsphere-Ramsey Theorem for Solvable Transitive Configurations

Dömötör Pálvölgyi

Abstract

Let P be a finite spherical set. We prove that if P admits a solvable group of isometries acting transitively on it, then every r-coloring of a sufficiently high-dimensional sphere of radius slightly larger than the circumradius of P contains a monochromatic congruent copy of P. Our proof builds on the group-theoretic argument of Kriz and combines it with a topological method that may be of independent interest.

Disclosure

“dition above. Acknowledgments I would like to thank Arsenii Sagdeev and Géza Tóth for several useful preliminary discussions, and Imre Bárány for pointing me to Szemerédi’s result in [9]. Statement on the use of artificial intelligence ChatGPT was used heavily in the preparation of this manuscript, although none of the main ideas underlying the ncs-Ramsey theorem originated from it. It contributed significantly to the proof of”
PDF page 25

Classification: Substantial proof generation
Multiplier: 10
Verified: 2026-08-23T05:09:26.455517Z

Structural counts

Pages 27 pdf

Theorems 6 source

Lemmas 7 source

Propositions 5 source

Corollaries 1 source

Definitions 3 source

Displayed equations 109 source

Bibliography entries 47 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file near_circumradius_ramsey_paper_v22.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.