{
  "abstract": "Counting the number of coverings of $s$ dimers on two-dimensional quadratic lattices is considered as intractable and belongs to \\#P-complete class. We reveal the structure of the exact solution to the problem and provide an explicit formula for it, which includes $s-1$ nesting sums. This results in an exponential time complexity of $O(2^s)$. The solution is explicitly determined by a sequence that exhibits double-exponential growth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19231",
  "author_total": 1,
  "authors": [
    {
      "name": "Yong Kong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9k13fhynadcx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19231",
  "fulltext_url": null,
  "id": "e9k13fhynadcx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19231",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213584933",
  "pdf_url": "https://arxiv.org/pdf/2609.19231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9k13fhynadcx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.19231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19231"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Intractable enumeration problems are like Russian nesting dolls: structural properties of monomer-dimer coverings on two-dimensional quadratic lattices",
  "title_text": "Intractable enumeration problems are like Russian nesting dolls: structural properties of monomer-dimer coverings on two-dimensional quadratic lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/e9k13fhynadcx",
  "venue": "arXiv",
  "versions": []
}