Cartesian products of two $CR$ sets
Combinatorics
2024-06-18 v2
Abstract
The notions of CR set is intimately related with the generalized van der Waerden's theorem. In this article, we prove the product of two CR sets is again a CR set. This answers [Question 4.2., N. Hindman, H. Hosseini, D. Strauss, and M. Tootkaboni: Combinatorially rich sets in arbitrary semigroups, Semigroup Forum, 107 (2023), 127-143.] . We use combinatorial arguments to prove our result.
Keywords
Cite
@article{arxiv.2402.09053,
title = {Cartesian products of two $CR$ sets},
author = {Sayan Goswami},
journal= {arXiv preprint arXiv:2402.09053},
year = {2024}
}
Comments
Semigroup Forum: to appear