{
  "abstract": "Fix $k\\ge 3$, and let $f_k(N)$ be the largest harmonic sum of a subset of $[N]$ containing no $k$ distinct integers with a common pairwise least common multiple. We prove that $f_k(N)=(\\log N)^{γ_k+o(1)}$ for a well-defined exponent $γ_k\\in(0,1]$. Following the weighted-pressure idea of Chojecki, we give a self-contained proof of variational formulas for $γ_k$ in terms of weighted sunflower-free families. We then eliminate the continuous weight: if $M_k(n,r)$ is the largest size of an $r$-uniform $k$-cosunflower-free family on $[n]$, then \\[ γ_k=\\sup_{n\\ge1,\\ 1\\le r\\le n}\\frac{r}{en}M_k(n,r)^{1/r}. \\] This finite-block formula yields a direct transfer principle from uniform set-system constructions, recovers the Tang--Zhang bounds, and gives $0.438899\\ldots<γ_3\\le0.889881\\ldots$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07268",
  "author_total": 3,
  "authors": [
    {
      "name": "Yanping Luo"
    },
    {
      "name": "Ruiyi Yang"
    },
    {
      "name": "Keheng Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fv7qnr5xmyn5h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07268",
  "fulltext_url": null,
  "id": "fv7qnr5xmyn5h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07268",
  "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": "W7212059601",
  "pdf_url": "https://arxiv.org/pdf/2609.07268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fv7qnr5xmyn5h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The exponent of harmonic LCM avoidance",
  "title_text": "The exponent of harmonic LCM avoidance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/fv7qnr5xmyn5h",
  "venue": "arXiv",
  "versions": []
}