{
  "abstract": "In this article, we show that the Sidon subsets of $[N]^d$ are Fourier uniform, and we prove a dense model lemma for Sidon sets. Using these results and a higher-dimensional version of Rado's theorem, we prove that given any partition regular linear equation in $s \\geq 5$ variables with nonzero coefficients, and any finite partition of a sufficiently dense Sidon subset $S$ of $[N]^d$, the number of monochromatic solutions to this equation is $\\gg |S|^s N^{-d}$ for all large $N$. As a corollary of the Fourier uniformity result, we show that dense Sidon subsets of $[N]^d$ are equidistributed in certain arithmetic and Bohr structures. Our proofs are motivated by the arguments of Ortega and Prendiville.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11840",
  "author_total": 1,
  "authors": [
    {
      "name": "Dev Ranjan Pandey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2sg3v8ahcxc6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11840",
  "fulltext_url": null,
  "id": "b2sg3v8ahcxc6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11840",
  "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"
    ]
  ],
  "openalex": "W7221164320",
  "pdf_url": "https://arxiv.org/pdf/2610.11840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2sg3v8ahcxc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Partition regular linear equations over Sidon sets",
  "title_text": "Partition regular linear equations over Sidon sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/b2sg3v8ahcxc6",
  "venue": "arXiv",
  "versions": []
}