{
  "abstract": "The set $A$ is a $B_h$-set if every element of the sumset $hA$ has a unique representation as a sum of $h$ elements of $A$. A $B_2$-set is also called a Sidon set. A $B_{h,Δ}$-set is a $B_h$-set $A$ whose sumset $hA$ is $Δ$-separated, that is, $|x-x'| \\geq Δ$ for all $x,x' \\in hA$ with $x\\neq x'$. Upper and lower bounds are obtained for the cardinality of the largest $B_{2,Δ}$-sets contained in $\\{1,2,\\ldots, n\\}$, that is, sets $A \\subseteq \\{1,2,\\ldots, n\\}$ such that, if $a,b,c,d \\in A$ and $\\{a,b\\} \\neq \\{c,d\\}$, then $|(a+b)-(c+d)| \\geq Δ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07416",
  "author_total": 1,
  "authors": [
    {
      "name": "Melvyn B. Nathanson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a4cse6wejahe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07416",
  "fulltext_url": null,
  "id": "9a4cse6wejahe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07416",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7202152964",
  "pdf_url": "https://arxiv.org/pdf/2608.07416",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a4cse6wejahe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.07416",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07416"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sidon sets with $Δ$-separated sumsets in additive number theory",
  "title_text": "Sidon sets with Δ-separated sumsets in additive number theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9a4cse6wejahe",
  "venue": "arXiv",
  "versions": []
}