Elsevier

Advances in Mathematics

Volume 321, 1 December 2017, Pages 269-286
Advances in Mathematics

Revisiting the nilpotent polynomial Hales–Jewett theorem

https://doi.org/10.1016/j.aim.2017.09.033Get rights and content
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Abstract

Answering a question posed by Bergelson and Leibman in [6], we establish a nilpotent version of the Polynomial Hales–Jewett Theorem that contains the main theorem in [6] as a special case. Important to the formulation and the proof of our main theorem is the notion of a relative syndetic set (relative with respect to a closed non-empty subsets of βG) [25]. As a corollary of our main theorem we prove an extension of the restricted van der Waerden Theorem to nilpotent groups, which involves nilprogressions.

Keywords

Polynomial Hales–Jewett Theorem
Ramsey theory
Algebra in the Stone–Čech compactification
Nilpotent groups
Nilprogressions
Syndetic sets

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