PreprintCC BY 4.0arXiv
A nearcircumsphere-Ramsey Theorem for Solvable Transitive Configurations
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.
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BibTeX
@misc{palvolgyi2026nearcircumsphereramsey,
title = {{A nearcircumsphere-Ramsey Theorem for Solvable Transitive Configurations}},
author = {Dömötör Pálvölgyi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.10865},
eprint = {2608.10865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10865},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A nearcircumsphere-Ramsey Theorem for Solvable Transitive Configurations
AU - Dömötör Pálvölgyi
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.10865
UR - https://arxiv.org/abs/2608.10865
AB - 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.
ER -