{
  "annotation_id": "70c96cd3-597d-44c8-826b-764b459e1050",
  "date_created": "2026-02-17T05:53:20.512000Z",
  "date_modified": "2026-02-17T05:53:20.512000Z",
  "file_hash": "db57af38bb07b3084946356294a387a49d9a87d848ccc3817509d13bc4b3ef85",
  "private": false,
  "record": {
    "abstract": "Given a graph $F$, the $r$-expansion $F^r$ of $F$ is the $r$-uniform hypergraph obtained from $F$ by inserting $r-2$ new distinct vertices in each edge of $F$. Given $r$-uniform hypergraphs $\\cH$ and $\\cF$, the generalized Tur\\\u0027{a}n number, denoted by $\\ex_r(n,\\cH,\\cF)$, is the maximum number of copies of $\\cH$ in an $n$-vertex $r$-uniform hypergraph that does not contain $\\cF$ as a subhypergraph. In the case where $r=2$ (i.e., the graph case), the study of generalized Tur\\\u0027{a}n problems was initiated by Alon and Shikhelman [\\textit{J. Combin. Theory Series B.} 121 (2016) 146--172]. Motivated by their work, we systematically study generalized Tur\\\u0027{a}n problems for expansions and obtain several general and exact results. In particular, for the non-degenerate case, we determine the exact generalized Tur\\\u0027{a}n number for expansions of complete graphs, and establish the asymptotics of the generalized Tur\\\u0027{a}n number for expansions of the vertex-disjoint union of complete graphs. For the degenerate case, we establish the asymptotics of generalized Tur\\\u0027{a}n numbers for expansions of several classes of forests, including star forests, linear forests and star-path forests.",
    "arxiv_id": "2601.09244",
    "authors": [
      "Junpeng Zhou",
      "Xiamiao Zhao",
      "Xiying Yuan"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On generalized Tur\\\u0027{a}n problems for expansions",
    "url": "https://arxiv.org/abs/2601.09244",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "54c9df21-f13a-4d1a-9727-9263397a5634",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}