{
  "abstract": "We denote by $f_k(Γ)$ the largest integer with the property that every subset of a finite abelian group $Γ$ of size at least $|Γ| - f_k(Γ)$ is a $k$-fold sumset. Extending a recent result of Alon and Pham, we prove that $$ f_k(Γ) \\leq \\widetilde{O} \\left(n^{(2k-1)/(4k-3)}\\right) $$ holds for all finite abelian groups $Γ$ and integers $k \\geq 2$, where $n = |Γ|$. Additionally, we also show that the lower bound $f_k(Γ) \\geq \\widetildeΩ \\left(n^{1/k}\\right)$ holds if $Γ$ has no nontrivial element of order dividing $k$. Our upper bound improves a previous result of Balogh, Liu, and Sharifzadeh, and recovers the bound of Alon and Pham in the case $k = 2$. The proof relies on a new upper bound for the independence number of random Cayley sum hypergraphs, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08629",
  "author_total": 2,
  "authors": [
    {
      "name": "Jihyo Chae"
    },
    {
      "name": "Hyunwoo Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b69pqr74rz1kz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08629",
  "fulltext_url": null,
  "id": "b69pqr74rz1kz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08629",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7220917664",
  "pdf_url": "https://arxiv.org/pdf/2610.08629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b69pqr74rz1kz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Random Cayley sum hypergraphs and $k$-fold sumsets",
  "title_text": "Random Cayley sum hypergraphs and k-fold sumsets",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:44Z",
  "url": "https://research.draconitic.com/paper/b69pqr74rz1kz",
  "venue": "arXiv",
  "versions": []
}