The sumsets tag has no wiki summary.

**6**

votes

**1**answer

141 views

### Iterated sumset inequalities in cancellative semigroups

This question is motivated by the following well-known theorems:
Thm (Plünnecke): If $A$ is a finite nonempty subset of an abelian group, then for every $n$ we have $|A^n| \le ...

**9**

votes

**0**answers

542 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 ...

**3**

votes

**0**answers

148 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 ...

**2**

votes

**0**answers

123 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 ...

**1**

vote

**0**answers

47 views

### $B_k[1]$ sets with smallest possible $m = max B_k[1]$ for given $k$ and $n = |B_k[1]|$ elements

Sidon sets are sets $A \subset \mathbb{N}$ such that for all $a_j,b_j \in A$ holds
$$a_1+a_2=b_1+b_2 \iff \{a_1,a_2\}=\{b_1,b_2\}$$
Thus if you know the sum of two elements, you know which elements ...