{
  "abstract": "Let $r,t\\ge 3$ be integers and $L=\\{\\ell_1,\\ell_2,\\ldots,\\ell_s\\}\\subseteq [0,r-1]$ a fixed set of integers with $|L|\\neq r$ and $\\ell_1<\\ell_2<\\cdots<\\ell_s$. For each integer $n$, let $Ψ_{r}(n,L,t)$ be the maximum number of $r$-cliques in an $n$-vertex graph whose $r$-cliques, viewed as a family of $r$-subsets of the vertex set, form a $t$-wise $L$-intersecting family. In this paper, we prove that $Ψ_{r}(n,L,t)=o(n^{|L|})$ when the sequence $\\ell_1,\\ell_2,\\ldots,\\ell_s,r$ does not form an arithmetic progression, and we give an asymptotic formula for $Ψ_{r}(n,L,t)$ when this sequence does form an arithmetic progression. When $t=2$, our results are exactly Helliar and Liu's results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22393",
  "author_total": 3,
  "authors": [
    {
      "name": "Yiyan Zhan"
    },
    {
      "name": "Yichen Wang"
    },
    {
      "name": "Mei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84f9cam4b9r4b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22393",
  "fulltext_url": null,
  "id": "84f9cam4b9r4b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22393",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214014755",
  "pdf_url": "https://arxiv.org/pdf/2609.22393",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84f9cam4b9r4b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22393",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22393"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting $t$-wise $L$-intersecting cliques with prescribed intersection sizes",
  "title_text": "Counting t-wise L-intersecting cliques with prescribed intersection sizes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/84f9cam4b9r4b",
  "venue": "arXiv",
  "versions": []
}