Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13974 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910576226074624 |
|---|---|
| author | Goswami, Sayan |
| author_facet | Goswami, Sayan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restricted van der Waerden theorem for nilprogressions Goswami, Sayan Combinatorics 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. |
| title | Restricted van der Waerden theorem for nilprogressions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.13974 |