arithmetic combinatorics

English

Noun

arithmetic combinatorics (uncountable)

1. (mathematics) A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
   • 2006, Terence Tao, Van H. Vu, Additive Combinatorics, Cambridge University Press, page 112:

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

   • 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:

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

   • 2019, Cain Mckay, Probability and Statistics, ED-Tech Press, page 23:

     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.

Related terms

• additive combinatorics

Translations

field of mathematics

• Armenian: թվաբանական կոմբինատորիկա (tʻvabanakan kombinatorika)

Further reading

• Szemerédi's theorem on Wikipedia.Wikipedia
• Problems involving arithmetic progressions on Wikipedia.Wikipedia