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Results tagged with additive-combinatorics
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user 21724
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.
6
votes
Accepted
Elementary Proof of Basis of Order k
If $B$ is a basis of order $k$ such that every integer $n$ can be written as a sum of $k$ elements from $B$ in $\asymp n^{o(1)}$ ways, then a simple counting argument yields $|B \cap [1 , X]| \asymp X …
- 7,249
12
votes
Sets of unit fractions with sum $\leq 1$
Let $R > 1$ and $\lambda \in \mathbb{R}$ be such that
$$
\int_{1}^R \mathrm{tanh}(\frac{\lambda x}{2}) \frac{d x}{x} = \log R -2.
$$
Then standard techniques in large deviation theory yield
$$
\frac{ …
- 7,249
4
votes
1
answer
696
views
A reference for this possibly well-known fact concerning the Kakeya conjecture?
I believe I have read or heard somewhere that the Kakeya conjecture would follow from appropriate lower bounds for the minimal size of a subset of $\{ 1 , \cdots , N\}$ which contains a translate of e …
- 7,249