7 problems

Schefler56Zhao56Zhong's conjecture. The support of $A$ has full size:

Let $r$ and $s$ be fixed positive integers. For a function $f:[n]\to\{-r,s\}$ with $f([n])=0$, let $M(r,s,k)$ denote the minimum threshold such that every sufficiently large $n$ fo…

Let $H$ be a transfer Krull monoid over a finite abelian group $G$, and let $\mathcal B(G)$ be the monoid of zero-sum sequences over $G$. Write $\mathsf L(a)$ for the set of factor…

Let $r$, $s$ and $k$ be positive integers such that $(r+s)$ divides $k$. A function $f:[n]\to\{-r,s\}$ has total sum $f([n])=0$ when the sum of its values over $[n]$ is zero. A ZS…

Systems-of-sets-of-lengths conjecture. If $G'$ is an abelian group satisfying

Structural conjecture. Each minimal zero-sum sequence $U$ over $G$ with $\mathsf{k}(U)=\mathsf{K}(G)$ has the form

Krause–Zahlten conjecture. The equality