"combinatorial geometry" meaning in English

See combinatorial geometry in All languages combined, or Wiktionary

Noun

Forms: combinatorial geometries [plural]
Etymology: From circa 1955. Head templates: {{en-noun|~}} combinatorial geometry (countable and uncountable, plural combinatorial geometries)
  1. (geometry, uncountable) The field of mathematics which examines extremal problems of a combinatorial nature expressed geometrically. Tags: uncountable Categories (topical): Geometry
    Sense id: en-combinatorial_geometry-en-noun-zzf6nuG3 Topics: geometry, mathematics, sciences
  2. (geometry, theory of matroids, countable) A simple matroid. Tags: countable Categories (topical): Geometry
    Sense id: en-combinatorial_geometry-en-noun-0P3-tcsf Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 33 67 Disambiguation of Entries with translation boxes: 16 84 Disambiguation of Pages with 1 entry: 24 76 Disambiguation of Pages with entries: 25 75 Topics: geometry, mathematics, sciences
The following are not (yet) sense-disambiguated
Related terms: combinatorial topology

Inflected forms

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  "etymology_text": "From circa 1955.",
  "forms": [
    {
      "form": "combinatorial geometries",
      "tags": [
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  "lang_code": "en",
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        {
          "ref": "2003, Lukas Finschi, Komei Fukuda, “Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements”, in Boris Aronov, Saugata Basu, Janos Pach, Micha Sharir, editors, Discrete and Computational Geometry, Springer,, page 425:",
          "text": "The generation of combinatorial types of point configurations and hyperplane arrangements point configurations and hyperplane arrangements has long been an outstanding problem of combinatorial geometry.",
          "type": "quote"
        },
        {
          "ref": "2006, Peter Brass, William O. J. Moser, János Pach, Research Problems in Discrete Geometry, Springer, page 183:",
          "text": "The following problem of Erdős [Er46] is possibly the best known (and simplest to explain) problem in combinatorial geometry. How often can the same distance occur among n points in the plane?",
          "type": "quote"
        },
        {
          "text": "2012, Mohammed Mostefa Mesmmoudi, et al., Discrete Curvature Estimation Methods for Triangulated Surfaces, Ullrich Köthe, Annick Montanvert, Pierre Soille (editors), Applications of Discrete Geometry and Mathematical Morphology, Springer, LNCS 7346, page 28,\nIn combinatorial geometry, the most common discrete representation for a surface is a triangle mesh."
        }
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        "The field of mathematics which examines extremal problems of a combinatorial nature expressed geometrically."
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        "(geometry, uncountable) The field of mathematics which examines extremal problems of a combinatorial nature expressed geometrically."
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          "text": "For the generation of these combinatorial types no direct method is known, and it appears to be necessary to use combinatorial abstractions — allowable sequences of permutations, #x5C;lambda-functions, chirotopes, combinatorial geometries, or oriented matroids; in our work we will use oriented matroids [BLVS⁺99].",
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          "ref": "2012, Don Row, Talmage James Reid, Geometry, Perspective Drawing, and Mechanisms, World Scientific, page 15:",
          "text": "Our purpose in this chapter is to derive fundamental properties of combinatorial geometries, and to show how these properties strengthen our intuitive understandings of figures.[…]In this section, we give an axiom system for combinatorial geometries and then prove that each combinatorial figure is a combinatorial geometry.",
          "type": "quote"
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  "wikipedia": [
    "Discrete geometry"
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  "word": "combinatorial geometry"
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          "text": "The generation of combinatorial types of point configurations and hyperplane arrangements point configurations and hyperplane arrangements has long been an outstanding problem of combinatorial geometry.",
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          "ref": "2006, Peter Brass, William O. J. Moser, János Pach, Research Problems in Discrete Geometry, Springer, page 183:",
          "text": "The following problem of Erdős [Er46] is possibly the best known (and simplest to explain) problem in combinatorial geometry. How often can the same distance occur among n points in the plane?",
          "type": "quote"
        },
        {
          "text": "2012, Mohammed Mostefa Mesmmoudi, et al., Discrete Curvature Estimation Methods for Triangulated Surfaces, Ullrich Köthe, Annick Montanvert, Pierre Soille (editors), Applications of Discrete Geometry and Mathematical Morphology, Springer, LNCS 7346, page 28,\nIn combinatorial geometry, the most common discrete representation for a surface is a triangle mesh."
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          "text": "For the generation of these combinatorial types no direct method is known, and it appears to be necessary to use combinatorial abstractions — allowable sequences of permutations, #x5C;lambda-functions, chirotopes, combinatorial geometries, or oriented matroids; in our work we will use oriented matroids [BLVS⁺99].",
          "type": "quote"
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          "ref": "2012, Don Row, Talmage James Reid, Geometry, Perspective Drawing, and Mechanisms, World Scientific, page 15:",
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.

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