Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are inverse problems: given the size...

arithmetic combinatorics in his review of "Additive Combinatorics" by Tao and Vu. Szemerédi's theorem is a result in arithmetic combinatorics concerning...

making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph...

Sawhney (Combinatorics, Massachusetts Institute of Technology), Cynthia Stoner (Combinatorics, Harvard University), Ashwin Sah (Combinatorics, Massachusetts...

In mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norms on functions on a finite group or group-like...

In additive combinatorics, the Ruzsa triangle inequality, also known as the Ruzsa difference triangle inequality to differentiate it from some of its variants...

the Erdős–Turán conjecture on additive bases. Shapley–Folkman lemma Additive combinatorics Multiplicative combinatorics Multiplicative number theory Nathanson...

In additive number theory and combinatorics, a restricted sumset has the form S = { a 1 + ⋯ + a n :   a 1 ∈ A 1 , … , a n ∈ A n   a n d   P ( a 1 , … ...

In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured...

often called Schur's property, also due to Issai Schur. The Wikibook Combinatorics has a page on the topic of: Proof of Schur's theorem In Ramsey theory...

graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence...

In additive combinatorics, the Plünnecke–Ruzsa inequality is an inequality that bounds the size of various sumsets of a set B {\displaystyle B} , given...

These questions are characteristic of arithmetic combinatorics, a coalescing field that subsumes additive number theory (which concerns itself with certain...

In additive combinatorics, the sumset (also called the Minkowski sum) of two subsets A {\displaystyle A} and B {\displaystyle B} of an abelian group G...

partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and...

Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory. Ergodic Ramsey theory arose shortly...

uncertainty. Additive combinatorics The part of arithmetic combinatorics devoted to the operations of addition and subtraction. Additive number theory...

ISBN 9783110283600 Green, Ben (2005), "Finite field models in additive combinatorics", Surveys in Combinatorics 2005, Cambridge University Press, pp. 1–28, arXiv:math/0409420...

was introduced in the 2010s but can be traced to older sources in additive combinatorics. Let G {\displaystyle G} be a group and K ≥ 1 {\displaystyle K\geq...

(1978), "Triple systems with no six points carrying three triangles", Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, Colloq. Math...

specialist in harmonic analysis, geometric measure theory, and additive combinatorics Carole Lacampagne, American mathematician known for her work in...

"A Multidimensional Szemerédi Theorem in the primes via Combinatorics". Annals of Combinatorics. 22 (4): 711–768. arXiv:1306.3025. doi:10.1007/s00026-018-0402-4...

In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose...

In mathematics, and in particular in arithmetic combinatorics, a Salem-Spencer set is a set of numbers no three of which form an arithmetic progression...

Euclidean harmonic analysis, analytic number theory, geometry and additive combinatorics. He is an assistant professor in the Department of Mathematics at...

constraints. Such questions arise naturally in extremal graph theory, additive combinatorics, discrete geometry, coding theory, and Ramsey theory; they include...

Hilbert’s 10th problem is undecidable for every ring of integers using additive combinatorics. Another team of mathematicians subsequently claimed another proof...

type of numerical sequence playing a role in ergodic theory and additive combinatorics. The concept is related to nilpotent Lie groups and almost periodicity...

Green's research is in the fields of analytic number theory and additive combinatorics, but he also has results in harmonic analysis and in group theory...

descriptions of redirect targets Gowers norm – Class of norms in additive combinatorics Kadec norm – All infinite-dimensional, separable Banach spaces are...