Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are inverse problems: given the size of the sumset A + B is small, what can we say about the structures of and ? In the case of the integers, the classical Freiman's theorem provides a partial answer to this question in terms of multi-dimensional arithmetic progressions.
Another typical problem is to find a lower bound for in terms of and . This can be viewed as an inverse problem with the given information that is sufficiently small and the structural conclusion is then of the form that either or is the empty set; however, in literature, such problems are sometimes considered to be direct problems as well. Examples of this type include the Erdős–Heilbronn Conjecture (for a restricted sumset) and the Cauchy–Davenport Theorem. The methods used for tackling such questions often come from many different fields of mathematics, including combinatorics, ergodic theory, analysis, graph theory, group theory, and linear algebraic and polynomial methods.
and 17 Related for: Additive combinatorics information
Additivecombinatorics is an area of combinatorics in mathematics. One major area of study in additivecombinatorics are inverse problems: given the size...
arithmetic combinatorics in his review of "AdditiveCombinatorics" 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...
In additivecombinatorics, the sumset (also called the Minkowski sum) of two subsets A {\displaystyle A} and B {\displaystyle B} of an abelian group G...
Terence; Vu, Van (2006). AdditiveCombinatorics. Cambridge Studies in Advanced Mathematics. Vol. 105. Cambridge University Press. "Additive number theory", Encyclopedia...
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...
ISBN 9783110283600 Green, Ben (2005), "Finite field models in additivecombinatorics", Surveys in Combinatorics 2005, Cambridge University Press, pp. 1–28, arXiv:math/0409420...
questions are characteristic of arithmetic combinatorics. This is a presently coalescing field; it subsumes additive number theory (which concerns itself with...
Euclidean harmonic analysis, analytic number theory, geometry and additivecombinatorics. He is an assistant professor in the Department of Mathematics at...
(1978), "Triple systems with no six points carrying three triangles", Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, Colloq. Math...
Salem Prize (joint with Julian Sahasrabudhe) for contributions to additivecombinatorics and related fields, including her work on quantitative density theorems...
Ramsey theory is a branch of mathematics where problems motivated by additivecombinatorics are proven using ergodic theory. Ergodic Ramsey theory arose shortly...
Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics: CIRM Jean-Morlet Chair, Fall 2016. Springer. p. 185. ISBN 9783319749082...
Cambridge: Cambridge University Press. Tao, Terence & Vu, Van (2006), AdditiveCombinatorics, Cambridge University Press. Mayer, A.; Zelenyuk, V. (2014). "Aggregation...
uncertainty. Additivecombinatorics The part of arithmetic combinatorics devoted to the operations of addition and subtraction. Additive number theory...
Global Information
