3 problems

Fan–Tringali conjecture. Every nonempty finite subset of $\mathbb{N}_{\geq 2}$ occurs as a length set in each of the power monoids $\mathcal{P}_{{\rm fin}}(\mathbb{N}_0)$ and…

Let $H$ be a monoid that is not torsion, and let $\mathcal P_{\mathrm{fin},1}(H)$ be its finitary power monoid containing the identity. A length set is the set of factorization len…

Let $G$ be a finite abelian group with $|G|>4$. Write $\rho(G)$ for its elasticity and let $Delta{rho}(G)$ be the set of all $dinmathbb N$ such that, for every $kinmathbb N$, ther…