{
  "abstract": "Nathanson observed that, for four-element sets $A$ of integers, the most frequent sizes of the iterated sumset $hA$ are separated by triangular numbers. Senger proved this and suggested an analogue for larger sets. We establish this pattern for $k$-element subsets of $\\{1,\\ldots,q\\}$, for every fixed $k\\geq3$, where $h\\geq2$ is either fixed or grows slower than $q^{1/(2k-1)}$. As $q\\to\\infty$, almost every such set has the largest possible $h$-fold sumset, and almost every exception has one of $h-1$ explicit smaller sizes. The differences between consecutive sizes among these $h$ values are consecutive $(k-2)$-dimensional simplex numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07303",
  "author_total": 5,
  "authors": [
    {
      "name": "Saad A. Awan"
    },
    {
      "name": "Steven J. Miller"
    },
    {
      "name": "Linh Nguyen"
    },
    {
      "name": "Steven Senger"
    },
    {
      "name": "Elvis Wong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/35y14zaky67n4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07303",
  "fulltext_url": null,
  "id": "35y14zaky67n4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07303",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/35y14zaky67n4.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Gaps in the Most Frequent Sizes of Integer Sumsets",
  "title_text": "Gaps in the Most Frequent Sizes of Integer Sumsets",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/35y14zaky67n4",
  "venue": "arXiv",
  "versions": []
}