{
  "abstract": "We show that for any finite partition of $\\mathbb{N}$ there is an infinite sequence whose finite sums are monochromatic and such that infinitely many of the products with a fixed number of factors are monochromatic -- though not necessarily belonging to the same color class as the finite sums. We are able to build these infinite configurations in parallel by refining arbitrary partitions of $\\mathbb{N}$. We apply these techniques to prove that many complex infinite sum-product configurations are guaranteed to be monochromatic for arbitrary finite colorings of $\\mathbb{N}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24751",
  "author_total": 1,
  "authors": [
    {
      "name": "Conner Griffin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cbv5nyk106e1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24751",
  "fulltext_url": null,
  "id": "9cbv5nyk106e1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24751",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7162398501",
  "pdf_url": "https://arxiv.org/pdf/2605.24751",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cbv5nyk106e1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2605.24751",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24751"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Infinite Sum-Product Configurations in Parallel",
  "title_text": "Infinite Sum-Product Configurations in Parallel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9cbv5nyk106e1",
  "venue": "arXiv",
  "versions": []
}