11 problems

Gallardo–Grekos–Pihko conjecture. There is a constant $c$ such that, whenever

Small-set restricted-sumset conjecture. If

Bounded-degree restricted-sumset conjecture. If the maximum degree of $\mathcal{R}$ on $B$ is at most $\Delta$, then

Lev's conjecture.

Lev–Freiman conjecture. One has

Let $G$ be an abelian group, and let $p$ be the smallest prime divisor of the order of $G$. For positive integers $m$ and $h$ with $m\leq p$, write $\rho\hat{\;} (G,m,h)$ for the m…

Let $G$ be an additive group with $|G|>1$. For finite subsets $A_1,\ldots,A_n$ of $G$, define … and … Let $n>1$ and assume that $|A_i|>1$ for every $i=1,\ldots,n$. The Sun restrict…

Let $n$ be a positive integer and let $m\leq n$. For an $m$-subset $A$ of $\mathbb{Z}_n$, write $\Sigma A=\bigcup_{h=0}^{\infty}h\hat{\;}A$ for its restricted sumset over all numbe…

Let $G$ be a finite abelian group of order $n$, let $p$ be the smallest prime divisor of $n$, and let $A$ be an $m$-subset of $G$. Inverse restricted-sumset conjecture. If…

Let $G$ be a finite abelian group of order $n$, let $p$ be the smallest prime divisor of $n$, and let $\rho\hat{\;} (G,m,h)$ denote the minimum restricted $h$-fold sumset size amon…

Let $\mathbb{Z}_n$ be the cyclic group of order $n$. For an $m$-subset of $\mathbb{Z}_n$, let $\rho\hat{\;} (\mathbb{Z}_n,m,h)$ denote the minimum size of its restricted $h$-fold s…