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arXiv · 0809.1709

Arithmetic Progressions in Abundance by Combinatorial Tools

Mathias Beiglboeck
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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.

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Mathias Beiglboeck. 2008-09-10. Arithmetic Progressions in Abundance by Combinatorial Tools. https://arxiv.org/abs/0809.1709

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