English

Monochromatic Regular Polygons in finitely colored $\mathbb{Z}_2 *\mathbb{Z}_2 *\mathbb{Z}_2$

Combinatorics 2018-07-26 v1 Dynamical Systems

Abstract

We show that for any finite coloring of the group Z2Z2Z2\mathbb{Z}_2 *\mathbb{Z}_2 *\mathbb{Z}_2 and for any positive integer kk, there always exists a monochromatic regular kk-gon in Z2Z2Z2\mathbb{Z}_2 *\mathbb{Z}_2 *\mathbb{Z}_2 with respect to the word length metric induced by the standard generating set; the edge length of which is estimated.

Keywords

Cite

@article{arxiv.1807.09411,
  title  = {Monochromatic Regular Polygons in finitely colored $\mathbb{Z}_2 *\mathbb{Z}_2 *\mathbb{Z}_2$},
  author = {Hui Xu and Enhui Shi},
  journal= {arXiv preprint arXiv:1807.09411},
  year   = {2018}
}
R2 v1 2026-06-23T03:13:25.672Z