{
  "id": "2402.09053",
  "version": "v2",
  "published": "2024-02-14T09:52:14.000Z",
  "updated": "2024-06-16T11:21:14.000Z",
  "title": "Cartesian products of two $CR$ sets",
  "authors": [
    "Sayan Goswami"
  ],
  "comment": "Semigroup Forum: to appear",
  "categories": [
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-16T11:21:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "22A15",
      "54D35"
    ],
    "keywords": [
      "cartesian products",
      "cr set",
      "generalized van der waerdens theorem",
      "combinatorial arguments",
      "combinatorially rich sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}