{
  "id": "2211.00766",
  "version": "v1",
  "published": "2022-11-01T22:13:46.000Z",
  "updated": "2022-11-01T22:13:46.000Z",
  "title": "Monochromatic Sums and Products of Polynomials",
  "authors": [
    "Ryan Alweiss"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We show that the pattern $\\{x,x+y,xy\\}$ is partition regular over the space of formal polynomials of degree at least one. This generalizes and provides a new proof of Moreira's celebrated result on the partition regularity of $\\{x,x+y,xy\\}$ over $\\mathbb{N}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-01T22:13:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monochromatic sums",
      "partition regularity",
      "moreiras celebrated result",
      "formal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}