{
  "abstract": "We determine, up to a factor of $2^{o(k)}$, the number of $k$-sets $A \\subset \\{1, \\ldots, n\\}$ such that $|A + A| \\leq m$, where $k = Θ(\\log n)$ and $m \\leq k^{1 + α}$, for small $α> 0$, answering a question of Green and Morris.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05384",
  "author_total": 3,
  "authors": [
    {
      "name": "Marcelo Campos"
    },
    {
      "name": "Gabriel Dahia"
    },
    {
      "name": "João Pedro Marciano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/849drf13jvfmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05384",
  "fulltext_url": null,
  "id": "849drf13jvfmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05384",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7211880686",
  "pdf_url": "https://arxiv.org/pdf/2609.05384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/849drf13jvfmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.05384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting sets with given doubling via dimension",
  "title_text": "Counting sets with given doubling via dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/849drf13jvfmj",
  "venue": "arXiv",
  "versions": []
}