{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Statement\n\nIn extremal set theory, the **Ahlswede–Khachatrian theorem** generalizes the Erdős–Ko–Rado theorem to $t$-intersecting families. Given parameters $n$, $k$ and $t$, it describes the maximum size of a $t$-intersecting family of subsets of $\\{1,\\dots,n\\}$ of size $k$, as well as the families achieving the maximum size.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "4BF3XCE5Z5"
    ],
    "kind": "statement",
    "name": "Ahlswede–Khachatrian theorem",
    "role": "proposition",
    "same_as": {
      "wikidata": "Q123881455",
      "wikipedia": "Ahlswede–Khachatrian theorem"
    },
    "sources": [
      {
        "locator": "Ahlswede–Khachatrian theorem",
        "mention": "wikipedia://en/75465176",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:75465176@r1369030983"
      }
    ],
    "tag": "SPECV9X1JE"
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/SPECV9X1JE/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/SPECV9X1JE.md",
  "msc": null,
  "name": "Ahlswede–Khachatrian theorem",
  "prov": null,
  "role": "proposition",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/SPE/SPECV9X1JE.md",
  "status": null,
  "tag": "SPECV9X1JE",
  "uri": "m2://SPECV9X1JE",
  "url": "https://math2.tamnd.com/wiki/ahlswede-khachatrian-theorem/",
  "writing": {
    "tag": "SPECV9X1JE",
    "kind": "statement",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "note": "each definition that the statement needs",
        "have": 0,
        "want": 1
      }
    ]
  }
}
