{
  "abstract": "For an integer $k$ and a set of integers $L$, a $(k,L)$-system is a family of $k$-element sets such that the size of the intersection of any two distinct members belongs to $L$. Let $m(n,k,L)$ denote the maximum size of a $(k,L)$-system on a ground set of $n$ elements. In this work, we establish a close connection between the asymptotic growth of $m(n,k,L)$ and almost entropic matroids. As a consequence, we obtain a general computable upper bound on the asymptotics of $m(n,k,L)$ that unifies and strengthens all previously known upper bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27892",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrey Kupavskii"
    },
    {
      "name": "Nikolai Terekhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3vp52shedpdz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27892",
  "fulltext_url": null,
  "id": "e3vp52shedpdz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27892",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223133479",
  "pdf_url": "https://arxiv.org/pdf/2610.27892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3vp52shedpdz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Almost entropic matroids and $(k,L)$-systems",
  "title_text": "Almost entropic matroids and (k,L)-systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/e3vp52shedpdz",
  "venue": "arXiv",
  "versions": []
}