9 problems

Archdeacon–Dinitz–Mattern–Stinson conjecture. For any cyclic group $\mathbb{Z}_n$ and any subset $A\subseteq\mathbb{Z}_n\setminus\{0\}$, there is an ordering of the elements of $A$…

Let $k$ be fixed, and let $A$ be a $k$-element subset of the nonzero elements of ${\mathbb Z}_n$. Fixed-size sequencing problem. Determine whether there exists a constant $N$ such…

CMPP conjecture. There exists an ordering of the elements of $A$ such that all partial sums are distinct.

G-ADMS conjecture. There exists an ordering of the elements of $A$ such that all partial sums are distinct.

Koumandos–Ruscheweyh weaker conjecture. For every $z\in\mathbb{D}$, $n\in\mathbb{N}$, and $0<\mu\leq\mu^{\ast}(\rho)$,

Let $(G,+)$ be an abelian group, and let $A$ be a finite subset of $G\setminus\{0\}$. Assume that no two-element subset $\{x,-x\}$ is contained in $A$, and that … For an ordering…

Let $A$ be a $k$-element subset of the nonzero elements of ${\mathbb Z}_n$, and let the partial-sum sequencing conjecture be the assertion that $A$ has an ordering with pairwise di…

Let $p$ be a prime and let $S$ be a multiset containing $p-1$ nonzero elements of ${\mathbb Z}_p$. Buratti's conjecture. There exists an arrangement of the elements of $S$ such tha…

Let $A=a_1,ots,a_k$ be a subset of the nonzero elements of ${\mathbb Z}_n$. For an ordering $(a_1,\ldots,a_k)$ of $A$, define the partial sums by … with arithmetic in…