"poset" meaning in English

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "Q538846"
      },
      "expansion": "Coined by American mathematician Garrett Birkhoff",
      "name": "coinage"
    }
  ],
  "etymology_text": "Abbreviation of partially ordered set. Coined by American mathematician Garrett Birkhoff in his Lattice Theory.",
  "forms": [
    {
      "form": "posets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "poset (plural posets)",
      "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 3 entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "algebraic poset"
        }
      ],
      "examples": [
        {
          "text": "1973, Barbara L. Osofsky, Homological Dimensions of Modules, American Mathematical Society, →ISBN, page 76,\n42. Definition. A poset (partially ordered set) (X, ≤) (usually written just X) is a set X together with a transitive, antisymmetric relation ≤ on X.\n43. Definition. A linearly ordered set or chain is a poset (X, ≤), such that ∀a, b ∈ X, either a ≤ b or b ≤ a or a = b."
        },
        {
          "text": "1998, Yuri A. Drozd, Representations of bisected posets and reflection functors, Idun Reiten, Sverre O. Smalø, Øyvind Solberg (editors), Algebras and Modules II, American Mathematical Society (for Canadian Mathematical Society), page 153,\nWe construct a complete set of reflection functors for the representations of posets and prove that they really have the usual properties. In particular, when the poset is of finite representation type, all of its indecomposable representations can be obtained from some \"trivial\" ones via relations. To define such reflection functors, a wider class of matrix problem is introduced, called \"representations of bisected posets\"."
        },
        {
          "ref": "1999, Manfred Stern, Semimodular Lattices: Theory and Applications, Cambridge University Press, page 189:",
          "text": "The combinatorial interest in posets is largely due to two unoriented graphs associated with a given poset: the comparability graph (which we shall not consider here) and the covering graph.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A partially ordered set."
      ],
      "id": "en-poset-en-noun--kN46LLW",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ]
      ],
      "raw_glosses": [
        "(set theory, order theory) A partially ordered set."
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "Partially ordered set"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈpəʊsɛt/"
    },
    {
      "audio": "LL-Q1860 (eng)-Vealhurl-poset.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/63/LL-Q1860_%28eng%29-Vealhurl-poset.wav/LL-Q1860_%28eng%29-Vealhurl-poset.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/63/LL-Q1860_%28eng%29-Vealhurl-poset.wav/LL-Q1860_%28eng%29-Vealhurl-poset.wav.ogg"
    }
  ],
  "word": "poset"
}

{
  "derived": [
    {
      "word": "algebraic poset"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "Q538846"
      },
      "expansion": "Coined by American mathematician Garrett Birkhoff",
      "name": "coinage"
    }
  ],
  "etymology_text": "Abbreviation of partially ordered set. Coined by American mathematician Garrett Birkhoff in his Lattice Theory.",
  "forms": [
    {
      "form": "posets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "poset (plural posets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English coinages",
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "English terms coined by Garrett Birkhoff",
        "English terms with quotations",
        "Pages with 3 entries",
        "Pages with entries",
        "en:Set theory"
      ],
      "examples": [
        {
          "text": "1973, Barbara L. Osofsky, Homological Dimensions of Modules, American Mathematical Society, →ISBN, page 76,\n42. Definition. A poset (partially ordered set) (X, ≤) (usually written just X) is a set X together with a transitive, antisymmetric relation ≤ on X.\n43. Definition. A linearly ordered set or chain is a poset (X, ≤), such that ∀a, b ∈ X, either a ≤ b or b ≤ a or a = b."
        },
        {
          "text": "1998, Yuri A. Drozd, Representations of bisected posets and reflection functors, Idun Reiten, Sverre O. Smalø, Øyvind Solberg (editors), Algebras and Modules II, American Mathematical Society (for Canadian Mathematical Society), page 153,\nWe construct a complete set of reflection functors for the representations of posets and prove that they really have the usual properties. In particular, when the poset is of finite representation type, all of its indecomposable representations can be obtained from some \"trivial\" ones via relations. To define such reflection functors, a wider class of matrix problem is introduced, called \"representations of bisected posets\"."
        },
        {
          "ref": "1999, Manfred Stern, Semimodular Lattices: Theory and Applications, Cambridge University Press, page 189:",
          "text": "The combinatorial interest in posets is largely due to two unoriented graphs associated with a given poset: the comparability graph (which we shall not consider here) and the covering graph.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A partially ordered set."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ]
      ],
      "raw_glosses": [
        "(set theory, order theory) A partially ordered set."
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "Partially ordered set"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈpəʊsɛt/"
    },
    {
      "audio": "LL-Q1860 (eng)-Vealhurl-poset.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/63/LL-Q1860_%28eng%29-Vealhurl-poset.wav/LL-Q1860_%28eng%29-Vealhurl-poset.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/63/LL-Q1860_%28eng%29-Vealhurl-poset.wav/LL-Q1860_%28eng%29-Vealhurl-poset.wav.ogg"
    }
  ],
  "word": "poset"
}