arithmetic combinatorics

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, 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.

• additive combinatorics

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