{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nThe $a$-**weight** of a string, for a letter $a$, is the number of times that letter occurs in the string. More precisely, let $A$ be a finite set (called the *alphabet*), $a\\in A$ a *letter* of $A$, and $c\\in A^*$ a *string* (where $A^*$ is the free monoid generated by the elements of $A$, equivalently the set of strings, including the empty string, whose letters are from $A$). Then the $a$-*weight* of $c$, denoted by $\\mathrm{wt}_a(c)$, is the number of times the generator $a$ occurs in the unique expression for $c$ as a product (concatenation) of letters in $A$.\n",
  "commit": "a799a9852bcfeae9dc83faa3bef60208bb53686b",
  "front": {
    "inventory": [
      "Y14G9VJ91D"
    ],
    "kind": "concept",
    "name": "Weight (strings)",
    "same_as": {
      "wikidata": "Q7979859",
      "wikipedia": "Weight (strings)"
    },
    "sources": [
      {
        "locator": "Weight (strings)",
        "mention": "wikipedia://en/6417882",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:6417882@r921563850"
      }
    ],
    "tag": "TKBPPBP9C6"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/TKBPPBP9C6/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/TKBPPBP9C6.md",
  "msc": null,
  "name": "Weight (strings)",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/TKB/TKBPPBP9C6.md",
  "status": null,
  "tag": "TKBPPBP9C6",
  "uri": "m2://TKBPPBP9C6",
  "url": "https://math2.tamnd.com/wiki/weight-strings/",
  "writing": {
    "tag": "TKBPPBP9C6",
    "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
      }
    ]
  }
}