"Sperner family" meaning in All languages combined

See Sperner family on Wiktionary

Noun [English]

Forms: Sperner families [plural]
Etymology: Named after Emanuel Sperner. Head templates: {{en-noun}} Sperner family (plural Sperner families)
  1. (combinatorics) A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice over the power set of E. Wikipedia link: Emanuel Sperner Categories (topical): Combinatorics Synonyms: clutter, Sperner system
    Sense id: en-Sperner_family-en-noun-bNxrQ8aa Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: combinatorics, mathematics, sciences

Inflected forms

{
  "etymology_text": "Named after Emanuel Sperner.",
  "forms": [
    {
      "form": "Sperner families",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Sperner family (plural Sperner families)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Combinatorics",
          "orig": "en:Combinatorics",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice over the power set of E."
      ],
      "id": "en-Sperner_family-en-noun-bNxrQ8aa",
      "links": [
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "family",
          "family"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "set",
          "set"
        ],
        [
          "antichain",
          "antichain"
        ],
        [
          "power set",
          "power set"
        ]
      ],
      "raw_glosses": [
        "(combinatorics) A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice over the power set of E."
      ],
      "synonyms": [
        {
          "word": "clutter"
        },
        {
          "word": "Sperner system"
        }
      ],
      "topics": [
        "combinatorics",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Emanuel Sperner"
      ]
    }
  ],
  "word": "Sperner family"
}
{
  "etymology_text": "Named after Emanuel Sperner.",
  "forms": [
    {
      "form": "Sperner families",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Sperner family (plural Sperner families)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Combinatorics"
      ],
      "glosses": [
        "A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice over the power set of E."
      ],
      "links": [
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "family",
          "family"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "set",
          "set"
        ],
        [
          "antichain",
          "antichain"
        ],
        [
          "power set",
          "power set"
        ]
      ],
      "raw_glosses": [
        "(combinatorics) A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice over the power set of E."
      ],
      "synonyms": [
        {
          "word": "clutter"
        },
        {
          "word": "Sperner system"
        }
      ],
      "topics": [
        "combinatorics",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Emanuel Sperner"
      ]
    }
  ],
  "word": "Sperner family"
}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-02-22 from the enwiktionary dump dated 2025-02-02 using wiktextract (9e2b7d3 and f2e72e5). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.