{
  "abstract": "Balogh, Bollobás and Narayanan conjectured that among all finite simple $r$-uniform $d$-regular hypergraphs, the number of weak independent sets is maximized by a natural quasi-bipartite construction $H_{r,d}$. We give three types of evidence for this conjecture. For every fixed $r$, we prove the conjectured asymptotic exponential rate whenever the twin quotient has maximum pair codegree $o(d)$. The proof uses the hypergraph container method. For hypergraphs with no cross-edges, the occupancy method gives the sharper error bound $O_r(\\log d/d)$. We show that a stronger version of the conjecture in terms of the so-called occupancy fraction is not true, by providing a counterexample for every $r\\ge 3$. We also prove exact cases of the conjecture when the hypergraph is $2$-regular. Using an entropy decomposition in the dual edge-cover problem, we settle every odd $r$ and the case $(r,d)=(4,2)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17468",
  "author_total": 3,
  "authors": [
    {
      "name": "Michail Sarantis"
    },
    {
      "name": "Prasad Tetali"
    },
    {
      "name": "Zeyu Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdb3ez9r6yap1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17468",
  "fulltext_url": null,
  "id": "cdb3ez9r6yap1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17468",
  "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|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213426594",
  "pdf_url": "https://arxiv.org/pdf/2609.17468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdb3ez9r6yap1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Counting Independent Sets in Regular Hypergraphs",
  "title_text": "On Counting Independent Sets in Regular Hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/cdb3ez9r6yap1",
  "venue": "arXiv",
  "versions": []
}