3 problems

The catenary-degree equality conjecture. For every group $G$ with

Let $M$ be the generalized arithmetic monoid under consideration, let $m\in M$, and let $\mathcal Z(m)$ be its set of factorizations. For factorizations $z,z'\in\mathcal Z(m)$, wri…

Let $M$ be the generalized arithmetic monoid under consideration, with parameters $h$ and $d$, and let $c(M)$, $c_{mon}(M)$, and $c_{eq}(M)$ denote its regular, monotone, and equiv…