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Results tagged with additive-combinatorics
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user 527577
Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
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Lower bound for restricted sumset in ordered groups
Recently in The restricted sumsets in finite abelian groups it is proved that
Suppose that $k \geq 2$ and $A$ is a non-empty subset of a finite abelian
group $G$ with $|G| > 1$. Then the cardinality …
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A problem on additive combinatorics in right-ordered groups
In a paper Small doubling in ordered groups: generators and structure it is proven in Lemma 4 page no. 598 that:
Let $G$ be an ordered group. Let $S$ be a finite subset of $G$ with at least two eleme …