• DOI:10.2989/16073606.2010.490992
• Corpus ID: 121697627

Ramsey Functions for Symmetric Subsets in Compact Abelian Groups

@article{Korostenski2010RamseyFF,
  title={Ramsey Functions for Symmetric Subsets in Compact Abelian Groups},
  author={Mareli Korostenski and Yuliya Zelenyuk},
  journal={Quaestiones Mathematicae},
  year={2010},
  volume={33},
  pages={161 - 169},
  url={https://api.semanticscholar.org/CorpusID:121697627}
}

• M. Korostenski, Y. Zelenyuk
• Published 6 July 2010
• Mathematics
• Quaestiones Mathematicae

Abstract Given a compact group G and r ∈ N, let sr(G) denote the least upper bound of real ϵ > 0 such that for every measurable r-coloring of G, there exists a monochrome symmetric subset of measure ≥ ϵ. A subset A ⊆ G is symmetric if there exists g ∈ G such that gA −1 g = A. We give a general picture of asymptotic behaviour of the function sr(G) for compact Abelian groups. 

Abstract Given a compact group G and r ∈ N, let sr(G) denote the least upper bound of real ϵ > 0 such that for every measurable r-coloring of G, there exists a monochrome symmetric subset of measure ≥ ϵ. A subset A ⊆ G is symmetric if there exists g ∈ G such that gA −1 g = A. We give a general picture of asymptotic behaviour of the function sr(G) for compact Abelian groups.