12 problems

Relative Davenport equality conjecture. One has

Monotonicity conjecture. One has

Asymptotic ball Davenport conjecture. For $m\geq\sqrt d$,

Optimal-support conjecture. Using an optimal distribution of the $d+1$ points on the $(d-1)$-sphere in dimension $d$, and charging these points adequately, gives the value of…

Two-dimensional box Davenport conjecture. For every integer $m\geq 2$,

Let $p$ be an odd prime and let … where ${\rm ord}_p(g)=p-1$. Holomorph f-constant conjecture. … This is the specialization of the preceding conjecture to the holomorph of…

Bass's conjecture. The Davenport constant of $G_{a,b,g}$ is

Erdős's conjecture. Every finite abelian group satisfies

For an integer $n>1$, let $I_r(\mathbb{Z}/n\mathbb{Z})$ denote the Erdős–Burgess constant of the multiplicative semigroup $\mathbb{Z}/n\mathbb{Z}$, let $\mathsf{D}(G)$ be the Daven…

Small Davenport constant upper-bound conjecture. The small Davenport constant satisfies

Let $G$ be a finite abelian group, and let $\mathsf{r}(G)$ denote its rank. The Davenport constant gap conjecture. … Here $\mathsf{D}(G)$ is the Davenport constant and…

Let $G$ be a finite abelian group of rank three. The rank-three Davenport constant conjecture. … Here $\mathsf{D}(G)$ is the Davenport constant of $G$, and $\mathsf{D}^{\ast}(G)$ i…