Enumeration of monochromatic three term arithmetic progressions in two-colorings of cyclic groups
Combinatorics
2014-11-11 v4
Abstract
One of the toughest problems in Ramsey theory is to determine the existence of monochromatic arithmetic progressions in groups whose elements have been colored. We study the harder problem to not only determine the existence of monochromatic arithmetic progressions, but to also count them. We reformulate the enumeration in real algebraic geometry and then use state of the art computational methods in semidefinite programming and representation theory to derive sharp, or an explicit constant from sharp, lower bounds for the cyclic group of any order.
Keywords
Cite
@article{arxiv.1408.1058,
title = {Enumeration of monochromatic three term arithmetic progressions in two-colorings of cyclic groups},
author = {Erik Sjöland},
journal= {arXiv preprint arXiv:1408.1058},
year = {2014}
}
Comments
15 pages. Update v2: Fixed typos. Update v3: Fixed mistakes in the references. Update v4: Incorporated feedback