{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, the **Jordan–Pólya numbers** are the numbers that can be obtained by multiplying together one or more [[factorials|0XWG0JGDFW]], not required to be distinct from each other. For instance, $480$ is a Jordan–Pólya number because $480=2!\\cdot 2!\\cdot5!$. Every [[tree|062D9KXJB1]] has a number of symmetries that is a Jordan–Pólya number, and every Jordan–Pólya number arises in this way as the [[order|0B85S2V2DR]] of an [[automorphism group|0CWXCWP0Y0]] of a tree. These numbers are named after Camille Jordan and George Pólya, who both wrote about them in the context of symmetries of trees.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "JHH0R8QKAR"
    ],
    "kind": "concept",
    "name": "Jordan–Pólya number",
    "same_as": {
      "wikidata": "Q108899013",
      "wikipedia": "Jordan–Pólya number"
    },
    "sources": [
      {
        "locator": "Jordan–Pólya number",
        "mention": "wikipedia://en/68857410",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:68857410@r1370496140"
      }
    ],
    "tag": "5YHKW9RJZY"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/5YHKW9RJZY/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/5YHKW9RJZY.md",
  "msc": null,
  "name": "Jordan–Pólya number",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/5YH/5YHKW9RJZY.md",
  "status": null,
  "tag": "5YHKW9RJZY",
  "uri": "m2://5YHKW9RJZY",
  "url": "https://math2.tamnd.com/wiki/jordan-polya-number/",
  "writing": {
    "tag": "5YHKW9RJZY",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
