{
  "abstract": "For a positive integer $h$, a subset $A = \\{a_1, \\dots, a_k\\}$ of an additive abelian group $G$ is called an $S_h$-set of size $k$ if all sums of $h$ distinct elements in $S$ are distinct. For fixed positive integers $h$ and $k$, let $v_h(k)$ denote the order of the smallest abelian group containing an $S_h$-set of size $k$. A lower bound for $v_2(k)$ is known. In this paper, we establish a lower bound for $v_3(k)$. Using our argument for $h=2$, we recover the known bound for $v_2(k)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12480",
  "author_total": 2,
  "authors": [
    {
      "name": "Vivekanand Goswami"
    },
    {
      "name": "Raj Kumar Mistri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h4m26ahewd5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12480",
  "fulltext_url": null,
  "id": "4h4m26ahewd5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12480",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212724229",
  "pdf_url": "https://arxiv.org/pdf/2609.12480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h4m26ahewd5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "$S_h$-sets in abelian groups",
  "title_text": "S_h-sets in abelian groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/4h4m26ahewd5s",
  "venue": "arXiv",
  "versions": []
}