{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, the **Johnson scheme**, named after Selmer M. Johnson, is also known as the triangular association scheme. It consists of the set of all binary vectors *X* of length *ℓ* and weight *n*, such that $v=\\left|X\\right|=\\binom{\\ell}{n}$. Two vectors *x*, *y* ∈ *X* are called *i*th associates if dist(*x*, *y*) = 2*i* for *i* = 0, 1, ..., *n*. The eigenvalues are given by\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "DV1ASN9KAY"
    ],
    "kind": "concept",
    "name": "Johnson scheme",
    "same_as": {
      "wikidata": "Q6268497",
      "wikipedia": "Johnson scheme"
    },
    "sources": [
      {
        "locator": "Johnson scheme",
        "mention": "wikipedia://en/22649423",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:22649423@r1169848354"
      }
    ],
    "tag": "HZ5CX9Y5W9"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/HZ5CX9Y5W9/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/HZ5CX9Y5W9.md",
  "msc": null,
  "name": "Johnson scheme",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/HZ5/HZ5CX9Y5W9.md",
  "status": null,
  "tag": "HZ5CX9Y5W9",
  "uri": "m2://HZ5CX9Y5W9",
  "url": "https://math2.tamnd.com/wiki/johnson-scheme/",
  "writing": {
    "tag": "HZ5CX9Y5W9",
    "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
      }
    ]
  }
}