arithmetic combinatorics

noun

A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.

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Meanings

nounarithmetic combinatorics (uncountable)
  1. uncountablemathematicsA field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.

    Some of the techniques involved^([with character sum problems]) belong to arithmetic combinatorics.

    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
    2 more examples

    For instance, progressions and lattices play a similar role in arithmetic combinatorics that balls and subspaces play in the theory of normed vector spaces.

    2006, Terence Tao, Van H. Vu, Additive Combinatorics, Cambridge University Press, page 112

    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.

    2019, Cain Mckay, Probability and Statistics, ED-Tech Press, page 23
Cite this entry
APA

arithmetic combinatorics. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/arithmetic%20combinatorics

MLA

“arithmetic combinatorics.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/arithmetic%20combinatorics. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “arithmetic combinatorics,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/arithmetic%20combinatorics.

Source: arithmetic combinatorics on Wiktionary, CC BY-SA 4.0.