{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, there are two natural interpretations of the **place-permutation action** of [[symmetric groups|0515A6D2Y1]], in which the group elements act on positions or *places*. Each may be regarded as either a left or a right action, depending on the order in which one chooses to compose [[permutations|05RWFKVTJ7]]. There are just two interpretations of the meaning of \"acting by a permutation $\\sigma$\" but these lead to four variations, depending whether maps are written on the left or right of their arguments. The presence of so many variations often leads to confusion. When regarding the group algebra of a symmetric group as a *diagram algebra* it is natural to write maps on the right so as to compute compositions of diagrams from left to right.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "G4B3DS47F2"
    ],
    "kind": "concept",
    "name": "Place-permutation action",
    "same_as": {
      "wikidata": "Q18388819",
      "wikipedia": "Place-permutation action"
    },
    "sources": [
      {
        "locator": "Place-permutation action",
        "mention": "wikipedia://en/43583184",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:43583184@r1178312647"
      }
    ],
    "tag": "1NXA9ARQD6"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/1NXA9ARQD6/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/1NXA9ARQD6.md",
  "msc": null,
  "name": "Place-permutation action",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/1NX/1NXA9ARQD6.md",
  "status": null,
  "tag": "1NXA9ARQD6",
  "uri": "m2://1NXA9ARQD6",
  "url": "https://math2.tamnd.com/wiki/place-permutation-action/",
  "writing": {
    "tag": "1NXA9ARQD6",
    "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
      }
    ]
  }
}