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Results tagged with additive-combinatorics
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user 35673
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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When does a Bohr set have the right size?
Fix a set $
\Gamma\subset \mathbb F_p$, the field with $p$ elements and a parameter $\epsilon>0$. The Bohr set $B(\Gamma,\epsilon)$ consists of those $x$ for which $x\cdot \Gamma\subseteq[-\epsilon p, …
- 133
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A (Hard?) combinatorial optimization problem involving the representation numbers
The trivial upper bound is in some sense best possible. Suppose I choose both partitions to consist of $p/N$ intervals of length $N$, say $[1,N],[N+1,2N],[(p-1)/N,p]$ (with a small error). Now given a …
- 133
1
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When does a Bohr set have the right size?
To some extent one can obtain upper bounds on $B(\Gamma,\epsilon)$ when $\Gamma$ is quite special. For instance, when $\Gamma$ is dissociated (which is to say, the sums $\sum_{s\in S}s$ are distinct f …
- 133