Cartesian products of two $CR$ sets
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917694620565504 |
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| author | Goswami, Sayan |
| author_facet | Goswami, Sayan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cartesian products of two $CR$ sets Goswami, Sayan Combinatorics 05D10, 22A15, 54D35 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. |
| title | Cartesian products of two $CR$ sets |
| topic | Combinatorics 05D10, 22A15, 54D35 |
| url | https://arxiv.org/abs/2402.09053 |