Questions tagged [sumsets]
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108 questions
13
votes
1
answer
572
views
Size of a certain sumset in $\mathbb{Z}/p^2\mathbb{Z}$
We are interested in estimating the size of a certain sumset in $\mathbb{Z}/p^2\mathbb{Z}$. Let $p$ be an odd prime, $g$ a primitive root modulo $p^2$, and $A=\langle g^p\rangle$ the unit subgroup of ...
- 165
1
vote
3
answers
350
views
how to proof this Stirling related equation
here is what I need to proof, have no idea were to start. I know there is some connection with the Stirling theorem.
$$
\sum_{i=0}^{d}\binom{m}{i} \leq \left ( \frac{em}{d} \right )^{d}
$$
I tried ...
- 11
11
votes
0
answers
830
views
Cliques in the Paley graph and a problem of Sarkozy
The following question is motivated by pure curiosity; it is not a part
of any research project and I do not have any applications. The question
comes as an interpolation between two notoriously ...
- 23k
4
votes
0
answers
216
views
Subgroup cliques in the Paley graph
It is a famous open problem to estimate non-trivially, for a prime $p\equiv 1\pmod 4$, the largest size of a subset $A\subset{\mathbb F}_p$ such that the difference of any two elements of $A$ is a ...
- 23k
4
votes
1
answer
864
views
Intersecting Hamming spheres: is $|A\stackrel k+E|\ge|A|$?
Since my original posting some ten days ago, I discovered an amazing
example which changed significantly my perception of the problem.
Accordingly, the whole post got re-written now.
The most general ...
- 23k
2
votes
0
answers
189
views
Doubling for Sumset of the same set
Let $G$ ($G=\mathbb{Z}^n_2$ for my case) be a additive group and $A$ be a subset of $G$. For any set $S\subseteq G$ define its doubling as $$\sigma (S)=\dfrac{|S+S|}{|S|}$$
Suppose $A$ has small ...
- 21
1
vote
1
answer
202
views
unique sums in a finite direct product of sets of integers
I am an algebraist, and I am wondering if there is a definition for the following:
Let $A_1$, $A_2$, $\ldots, A_n$ be sets of integers (or more generally, subsets of a group $G$). Say that (for the ...
- 11
1
vote
1
answer
234
views
Find an approximate expression of a sum of a product using the average of each item
Is it possible to find an approximate expression of $\frac{\sum_{i=1}^{n} k_i x_i}{\sum_{i=1}^{n} k_i}$ using $\langle k \rangle$, $\langle k^2 \rangle$, $\langle x \rangle$, and $n$? Alternatively if ...
- 185