7 problems

Let $m\geq 3$ and consider the regions arising in Algorithm for testing numerical semigroups of multiplicity $m$. Empty-region conjecture. For each $m\geq 3$, every region consider…

Cisto's Generalized Wilf conjecture. The inequality

Let $n\geq 2$, let $M=\mathbf P(n,\mathbb N)$, and let $S$ be a unipotent numerical monoid in $M$. Let $\varphi(S)$ be its image in $\mathbb N^{n-1}$ under the monoid isomorphism…

Let $n\geq 2$, and let $T$ be a generalized numerical monoid (GMS), meaning a complement-finite submonoid of $\mathbb N^{n-1}$. Let $H(T)=\mathbb N^{n-1}\setminus T$ be its hole se…

Let $G$ be a unipotent linear algebraic group, and let $M=G_{\mathbb N}$. Let $S$ be a unipotent numerical monoid in $M$, with relative conductor $\mathtt{c}_M(S)$, relative sporad…

Bound conjecture. For any semigroup $\Gamma$,

Frögoh"amosa conjecture. The equality