Arithmetic Progressions in Abundance by Combinatorial Tools
Combinatorics
2008-09-11 v1
Abstract
Using the algebraic structure of the Stone-Cech compactification of the integers, Furstenberg and Glasner proved that for arbitrary k, every piecewise syndetic set contains a piecewise syndetic set of k-term arithmetic progressions. We present a purely combinatorial argument which allows to derive this result directly from van der Waerden's Theorem.
Cite
@article{arxiv.0809.1709,
title = {Arithmetic Progressions in Abundance by Combinatorial Tools},
author = {Mathias Beiglboeck},
journal= {arXiv preprint arXiv:0809.1709},
year = {2008}
}