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Arithmetic combinatorics

Known as: Additive combinatorics, Multiplicative combinatorics 
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
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Related topics

Related topics

4 relations
Ergodic Ramsey theoryErgodic theoryInteger-valued polynomialShapley–Folkman lemma

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2018
2018
Fast Modular Subset Sum using Linear Sketching
Given n positive integers, the Modular Subset Sum problem asks if a subset adds up to a given target t modulo a given integer m… 
Highly Cited
2016
Highly Cited
2016
Structure of Protocols for XOR Functions
Let f be a boolean function on n variables. Its associated XOR function is the two-party function F(x, y) = f(x xor y). We show… 
2016
2016
Prescribing the binary digits of squarefree numbers and quadratic residues
We study the equidistribution of multiplicatively defined sets, such as the squarefree integers, quadratic non-residues or… 
2015
2015
An Exposition of Sanders' Quasi-Polynomial Freiman-Ruzsa Theorem
The polynomial Freiman-Ruzsa conjecture is one of the most important conjec- tures in additive combinatorics. It asserts that one… 
Highly Cited
2015
Highly Cited
2015
Super-linear gate and super-quadratic wire lower bounds for depth-two and depth-three threshold circuits
In order to formally understand the power of neural computing, we first need to crack the frontier of threshold circuits with two… 
Review
2013
Review
2013
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or… 
Highly Cited
2012
Highly Cited
2012
Some new inequalities in additive combinatorics
In the paper we find new inequalities involving the intersections $A\cap (A-x)$ of shifts of some subset $A$ from an abelian… 
2010
2010
EXPANSION OF ORBITS OF SOME DYNAMICAL SYSTEMS OVER FINITE FIELDS
Abstract Given a finite field 𝔽p={0,…,p−1} of p elements, where p is a prime, we consider the distribution of elements in the… 
Highly Cited
2009
Highly Cited
2009
The Degrees-of-Freedom of the $K$-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients
The degrees-of-freedom of a K-user Gaussian interference channel (GIC) has been defined to be the multiple of (1/2)log 2 P at… 
Review
2009
Review
2009
Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak
This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics… 
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