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Results tagged with additive-combinatorics
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user 37555
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.
4
votes
Accepted
Subset of the integers with certain properties
Dietmann and Elsholtz (Hilbert cubes in progression-free sets and in the set of squares, Israel J. Math. 192 (2012), 59–66) have shown that if $S\subseteq[1, x]$ is a set such that all subset sums are …
4
votes
The density of numbers of the form $p + 2^k$
Romani (Calcolo 20 (1983), 319 - 336) gave a heuristic argument leading to the conjecture that the asymptotic density should exist and should be about 0.434... .
The basic idea of the heuristics is th …
8
votes
Accepted
higher dimensional analogue of EGZ theorem
In higher dimension things become more complicated. For a finite abelian group $G$ define $\mathfrak{s}(G)$ to be the least integer $N$, such that every sequence $x_1, \ldots, x_N$ of elements of $G$ …
7
votes
Accepted
Two equivalent statements about primes
Statement a) is true for all $N$. This follows from the fact that the number of even integers which cannot be expressed as the sum of 2 primes is small. The best result in this direction is due to Pin …