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Results tagged with sumsets
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user 4312
10
votes
Accepted
Sumsets with distinct numbers, upper bound for maximum element
Set $A$, $|A|=n$, with $|A+A|=n(n+1)/2$, is known as a `Sidon set'. This is a subject of numerous studies. As for your specific question, $c_1n^2<S(n)<c_2 n^2$ for some absolute constants, but I do no …
- 109k
5
votes
Accepted
Equal subset-sums of bounded vectors
As I understand, your $n$ and $d$ are fixed, and you want to prove the existence of corresponding non-empty subsets $I$, $J$ provided that both $t$, $s$ are large enough (greater than some constant $C …
- 109k
2
votes
Accepted
Controlling iterated sum sets of "most" of $A+B$
For each element of $x\in A+B+nS$ we construct at least $(\frac{|A||B|}{2|A+B|})^n$ distinct sequences $(t_0,\ldots,t_n)\in (A+B)^{n+1}$ such that $x=t_0+\ldots+t_n$ (the sentence after "observe that. …
- 109k