English

A Ramsey-type phenomenon in two and three dimensional simplices

Combinatorics 2023-10-02 v1 Logic

Abstract

We develop a Ramsey-like theorem for subsets of the two and three-dimensional simplex. A generalization of the combinatorial theorem presented here to all dimensions would produce a new proof that Homeo+[0,1]\textrm{Homeo}_+[0,1] is extremely amenable (a theorem due to Pestov) using general results of Uspenskij on extreme amenability in homeomorphism groups.

Keywords

Cite

@article{arxiv.2309.17274,
  title  = {A Ramsey-type phenomenon in two and three dimensional simplices},
  author = {Sumun Iyer},
  journal= {arXiv preprint arXiv:2309.17274},
  year   = {2023}
}

Comments

16 pages

R2 v1 2026-06-28T12:36:09.833Z