"arithmetic combinatorics" meaning in English

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "arithmetic combinatorics (uncountable)",
      "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": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2006, Terence Tao, Van H. Vu, Additive Combinatorics, Cambridge University Press, page 112",
          "text": "For instance, progressions and lattices play a similar role in arithmetic combinatorics that balls and subspaces play in the theory of normed vector spaces.",
          "type": "quotation"
        },
        {
          "ref": "2016, Mei-Chu Chang, “Character sums and arithmetic combinatorics”, in Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, Prasad Tetali, editors, Recent Trends in Combinatorics, Springer,, page 405",
          "text": "Some of the techniques involved belong to arithmetic combinatorics.",
          "type": "quotation"
        },
        {
          "ref": "2019, Cain Mckay, Probability and Statistics, ED-Tech Press, page 23",
          "text": "Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis.[…]One important technique in arithmetic combinatorics is the ergodic theory of dynamical systems.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis."
      ],
      "id": "en-arithmetic_combinatorics-en-noun-wWMCxBf8",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "ergodic theory",
          "ergodic theory"
        ],
        [
          "harmonic analysis",
          "harmonic analysis"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis."
      ],
      "related": [
        {
          "word": "additive combinatorics"
        }
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "hy",
          "lang": "Armenian",
          "roman": "tʻvabanakan kombinatorika",
          "sense": "field of mathematics",
          "word": "թվաբանական կոմբինատորիկա"
        }
      ],
      "wikipedia": [
        "arithmetic combinatorics"
      ]
    }
  ],
  "word": "arithmetic combinatorics"
}

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "arithmetic combinatorics (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "additive combinatorics"
    }
  ],
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2006, Terence Tao, Van H. Vu, Additive Combinatorics, Cambridge University Press, page 112",
          "text": "For instance, progressions and lattices play a similar role in arithmetic combinatorics that balls and subspaces play in the theory of normed vector spaces.",
          "type": "quotation"
        },
        {
          "ref": "2016, Mei-Chu Chang, “Character sums and arithmetic combinatorics”, in Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, Prasad Tetali, editors, Recent Trends in Combinatorics, Springer,, page 405",
          "text": "Some of the techniques involved belong to arithmetic combinatorics.",
          "type": "quotation"
        },
        {
          "ref": "2019, Cain Mckay, Probability and Statistics, ED-Tech Press, page 23",
          "text": "Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis.[…]One important technique in arithmetic combinatorics is the ergodic theory of dynamical systems.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "ergodic theory",
          "ergodic theory"
        ],
        [
          "harmonic analysis",
          "harmonic analysis"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "arithmetic combinatorics"
      ]
    }
  ],
  "translations": [
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "tʻvabanakan kombinatorika",
      "sense": "field of mathematics",
      "word": "թվաբանական կոմբինատորիկա"
    }
  ],
  "word": "arithmetic combinatorics"
}