Restricted van der Waerden theorem for nilprogressions
Combinatorics
2024-08-27 v1
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 and conjectured that this result must hold for arbitrary rank. In this article, we give an affirmative answer to their conjecture.
Cite
@article{arxiv.2408.13974,
title = {Restricted van der Waerden theorem for nilprogressions},
author = {Sayan Goswami},
journal= {arXiv preprint arXiv:2408.13974},
year = {2024}
}