{
  "abstract": "Let $p_k(n)$ be the number of $k$-polymatroids on $[n]$. We show that for every fixed $k \\geq 1$, we have \\[ \\left\\lfloor \\frac{k}{2} \\right\\rfloor \\cdot \\binom{n}{\\lfloor n/2 \\rfloor} \\cdot (1+o(1)) \\le \\log_2 p_k(n) \\le k \\cdot \\binom{n}{\\lfloor n/2 \\rfloor} \\cdot (1+o(1)). \\] We also show that for $k \\geq 2$, almost all $k$-polymatroids are (i) connected, (ii) proper, and (iii) not linearly representable over any field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18225",
  "author_total": 2,
  "authors": [
    {
      "name": "Seonghyuk Im"
    },
    {
      "name": "Donggyu Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmtjgh90ypta2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18225",
  "fulltext_url": null,
  "id": "fmtjgh90ypta2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18225",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7203888495",
  "pdf_url": "https://arxiv.org/pdf/2608.18225",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmtjgh90ypta2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.18225",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18225"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the enumeration of polymatroids",
  "title_text": "On the enumeration of polymatroids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/fmtjgh90ypta2",
  "venue": "arXiv",
  "versions": []
}