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additive combinatorics

additive combinatorics noun: a subbranch of combinatorics that concerns additive problems expressed using sumsets.

Noun

additive combinatorics (uncountable)

  1. A subbranch of combinatorics that concerns additive problems expressed using sumsets.
    • One major area of study in additive combinatorics is that of inverse problems: for instance, given the sumset A#43;B is small in size, what can we say about the structures of A and B? In the case of integer sumsets, Freiman's theorem provides a partial answer.
    • 2007, Andrew Granville, Additive Combinatorics, American Mathematical Society, https://books.google.com.au/books?id=SOVPnwEACAAJ&dq=%22Additive+combinatorics%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwj5zJbJ0bLsAhUQX30KHTZYAZwQ6AEwRnoECBwQAg.
    Synonyms:
    discipline that concerns combinatorics problems expressed using sumsets

Examples of additive combinatorics in a sentence

  • We now discuss what appears at first glance to be an unrelated topic, namely that of additive combinatorics (and its noncommutative counterpart, multiplicative combinatorics).2014, Terence Tao, Hilbert's Fifth Problem and Related Topics, American Mathematical Society, page 14:
  • This book deals with additive combinatorics, a vibrant area of current mathematical research.2016, Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, Taylor & Francis (CRC Press), page xi:

Synonyms of additive combinatorics

  • discipline that concerns combinatorics problems expressed using sumsets

Origin of additive combinatorics

Coined circa early 2000s by Australian-American mathematician Terence Tao for a rapidly developing field growing out of combinatorial number theory, named differently to reflect a changed emphasis in the problems being studied.

Questions about additive combinatorics

What does additive combinatorics mean?
Additive combinatorics means a subbranch of combinatorics that concerns additive problems expressed using sumsets.
How do you use additive combinatorics in a sentence?
We now discuss what appears at first glance to be an unrelated topic, namely that of additive combinatorics (and its noncommutative counterpart, multiplicative combinatorics).
What part of speech is additive combinatorics?
Additive combinatorics is a noun.

Words near additive combinatorics in the dictionary

  1. additionists
  2. additions
  3. addititious
  4. additive
  5. additive category
  6. additive combinatorics
  7. additive function
  8. additive functions
  9. additive group
  10. additive groups
  11. additive identities

Source and license

Adapted from Wiktionary: additive combinatorics (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “additive combinatorics.” Word.ws, https://word.ws/additive_combinatorics. Based on Wiktionary, CC BY-SA 4.0.