Geodesic
Restricted van der Waerden theorem for nilprogressions
Sayan Goswami1
1University of kalyani
The electronic journal of combinatorics, Tome 32 (2025) no. 3
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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.
DOI : 10.37236/13512
Classification : 05D10, 05C55
Mots-clés : polynomial Hales-Jewett theorem, Ramsey theory

Sayan Goswami  1

1 University of kalyani 
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Sayan Goswami. Restricted van der Waerden theorem for nilprogressions. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13512

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