{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "5VDCJTZ8SW"
    }
  ],
  "body": "\n## Summary\n\nAlgebraic combinatorics uses methods of abstract algebra to study combinatorial structures, and combinatorial methods to study algebraic objects, see the [[definition|5VDCJTZ8SW]].\nCentral topics are [[symmetric functions|PAJEHWXW6M]], [[Young tableaux|Q6TH9PH2R7]] and the [[representation theory of the symmetric group|1VQC05EEYW]].\nOther topics are [[association schemes|C338GKB4VJ]], [[incidence algebras|1H9SFWHYEB]] of partially ordered sets, and the algebra of simplicial complexes.\nMany of its results are identities that have both an algebraic proof and a bijective proof.\n\n## Explanations\n\n### L1 human\n\nAlgebraic combinatorics is a two-way street between counting and algebra.\nIn one direction, a counting problem is solved by building a group, a ring or a matrix and computing with it.\nIn the other direction, an algebraic quantity, such as the dimension of a representation, is computed by counting pictures.\nFor example, the dimensions of the irreducible representations of the symmetric group are counted by standard Young tableaux.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "05E99",
      "05E05",
      "05E10"
    ],
    "name": "Algebraic combinatorics",
    "same_as": {
      "wikidata": "Q1005603",
      "wikipedia": "Algebraic combinatorics"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Algebraic_combinatorics"
      }
    ],
    "specializes": [
      "0JKW7W7XFR"
    ],
    "tag": "VPAQZ0XW74"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/VPAQZ0XW74/",
  "links": [
    {
      "field": "specializes",
      "target": "0JKW7W7XFR"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/VPAQZ0XW74.md",
  "msc": [
    "05E99",
    "05E05",
    "05E10"
  ],
  "name": "Algebraic combinatorics",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/VPA/VPAQZ0XW74.md",
  "status": null,
  "tag": "VPAQZ0XW74",
  "uri": "m2://VPAQZ0XW74",
  "url": "https://math2.tamnd.com/wiki/algebraic-combinatorics/",
  "writing": {
    "tag": "VPAQZ0XW74",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}