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arXiv · 2408.13974

Restricted van der Waerden theorem for nilprogressions

Sayan Goswami
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Abstract

In [Adv. Math., 321 (2017) 269-286], using the theory of ultrafilters, J. H. Johnson Jr., and F. K. Richter proved the nilpotent polynomial Hales-Jewett theorem. Using this result they proved the restricted version of the van der Waerden theorem for nilprogressions of rank $2$ and conjectured that this result must hold for arbitrary rank. In this article, we give an affirmative answer to their conjecture.

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Sayan Goswami. 2024-08-26. Restricted van der Waerden theorem for nilprogressions. https://arxiv.org/abs/2408.13974

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