10 problems

Let $T\subseteq \mathbb{Z}_v\setminus\{0\}$ satisfy … An ordering of the elements of $T$ is simple when its partial sums are all distinct and non-zero. Alspach's conjecture. Every…

Archdeacon's conjecture. An integer $\mathrm{H}(m,n;s;k)$ exists if and only if

Let $(G,+)$ be an abelian group, and let $T$ be a finite subset of $G\setminus\{0\}$ such that no $2$-subset $\{x,-x\}$ is contained in $T$ and … An ordering of the elements of $T$…

Let $T\subseteq \mathbb{Z}_v\setminus\{0\}$. An ordering of the elements of $T$ is simple when its partial sums are all distinct and non-zero. Graham–Archdeacon conjecture. The set…

Weak CMPP conjecture. If

Let $G$ be an abelian group and let $S$ be a finite subset of $G\setminus\{0\}$ such that … and $|S\cap\{x,-x\}|\leq1$ for every $x\in G$. Costa–Morini–Pasotti–Pellegrini conjectur…

Let $(G,+)$ be an abelian group. Let $A$ be a finite subset of $G\setminus\{0\}$ such that no $2$-subset $\{x,-x\}$ is contained in $A$, and suppose that … A simple ordering of $A$…

Let $n$ and $k$ be integers, and let $H(n;k)$ denote a square integer Heffter array of order $n$ with $k$ filled cells in each row and column. Existence conjecture. There exists an…

Full Heffter array conjecture. There exist Heffter arrays $H(m,n)$ for all $m,n\geq 3$. Moreover, they are integer Heffter arrays when $mn\equiv 0,3\pmod{4}$, and are shiftable whe…

Heffter array existence conjecture. There exists a Heffter array $H(m,n;s,t)$ for all $m,n,s,t$ with $s,t\geq 3$ and $ms=nt$. If the conditions of the necessary integer-sum lemma a…