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...ian group]]s and [[commutative semigroup]]s with an operation of addition. Additive number theory has close ties to [[combinatorial number theory]] and the [[g ==Additive number theory== ...

In [[additive combinatorics]], the '''sumset''' (also called the [[Minkowski addition|Minkowski sum]]) Many of the questions and results of additive combinatorics and [[additive number theory]] can be phrased in terms of sumsets. For example, [[Lagrange ...

...last2=Ginzburg | first2=A. | last3=Ziv | first3=A. | title=Theorem in the additive number theory | journal=Bull. Res. Council Israel | volume=10F | pages=41–4 ...ra (Coordinators of the DocCourse) | title=Combinatorial number theory and additive group theory | url=https://archive.org/details/combinatorialnum00gero_834 | ...

{{wikibooks|Combinatorics|Schur's Theorem|Proof of Schur's theorem}} == Combinatorics == ...

:Honorable mention: [[Maria Monks]] ([[Combinatorics]] and [[number theory]], [[Massachusetts Institute of Technology]]) :'''Winner:''' [[Maria Monks]] ([[Combinatorics]] and [[number theory]], [[Massachusetts Institute of Technology]])<ref>{{c ...

{{Short description|Method in enumerative combinatorics}} In the [[mathematics|mathematical]] field of [[enumerative combinatorics]], [[identity (mathematics)|identities]] are sometimes established by argum ...

...lf an area of [[mathematics]], that lies at the intersection of [[extremal combinatorics]] and [[graph theory]]. In essence, extremal graph theory studies how globa |article=Extremal and Probabilistic Combinatorics ...

* [[Rule of sum]], in combinatorics * [[Zero-sum problem]] in combinatorics ...

...c combinatorics]] (not to be confused with the [[Erdős–Turán conjecture on additive bases]]). It states that if the sum of the reciprocals of the members of a Formally, the conjecture states that if ''A'' is a [[Large set (combinatorics)|large set]] in the sense that ...

...e set|countable]] but countable groups need not be finitely generated. The additive group of [[rational number]]s '''Q''' is an example of a countable group th ...]]. Every infinite cyclic group is [[group isomorphism|isomorphic]] to the additive group of the [[Integer#Algebraic properties|integers]] '''Z'''. ...

A set of integers is said to be [[Small set (combinatorics)|small]] if the sum of its [[Multiplicative inverse|reciprocal]]s [[converg [[Category:Additive combinatorics]] ...

* The linear class '''''B''''' is '''additive''', that is, closed under repeated [[symmetric difference]] (when the resul .../view/Surveys ''Electronic Journal of Combinatorics'', Dynamic Surveys in Combinatorics, #DS8]. ...

| thesis_title = Topics in Arithmetic Combinatorics ...RS]] (born 27 February 1977) is a British mathematician, specialising in [[combinatorics]] and [[number theory]]. He is the [[Waynflete Professor of Pure Mathematic ...

*{{cite book| last=Nathanson | first=Melvyn B. | year=1996 | title=Additive Number Theory: Inverse Problems and Geometry of Sumsets | volume=165 | seri [[Category:Combinatorics]] ...

In [[additive combinatorics]], a discipline within mathematics, '''Freiman's theorem''' is a central re ...ref><ref>{{cite book| last=Nathanson | first=Melvyn B. | year=1996 | title=Additive Number Theory: Inverse Problems and Geometry of Sumsets | volume=165 | seri ...

| fields = [[Mathematical analysis|Analysis]] and [[Combinatorics]] ...l functions]], [[number theory]], [[mathematical analysis|analysis]] and [[combinatorics]]. ...

...92|loc=p. 331}}</ref> If <math>G</math> is an [[abelian group]] written in additive notation, the defining condition is that every non-zero element of <math>G< ..., and is called a '''translate''' of <math>D</math> (<math>D + g</math> in additive notation). ...

...rt constant]], in mathematics, an invariant of a group studied in additive combinatorics ...

| thesis_title = Extremal Problems in Combinatorics ...or of mathematics at Princeton University noted for his contributions to [[combinatorics]] and [[theoretical computer science]], having authored hundreds of papers. ...

*[[Additive function]] ==[[Analytic number theory]]: additive problems== ...