16 problems

Let $\b X$ be a formal curve with associated numerical monoid … For a numerical monoid, let the associated numerical monoid of a blowup be the numerical monoid corresponding to its…

Let $H$ be a numerical monoid, and for $k,l\in\mathbb N$ let $\alpha_{k,l}(H)$ be the number of $k$-element atoms of $\mathcal P_{\mathrm{fin},0}(H)$ whose maximum is at most $l$.…

Let $\mathscr{T}(e,m)$ and $\mathscr{D}(e,m)$ denote the functions defined in the paper for the type and the relevant upper bound of numerical monoids. Asymptotic strictness conjec…

A numerical monoid is a submonoid $S$ of $(\mathbb N,+)$ such that $\mathbb N\smallsetminus S$ is finite. Let the reduced power monoid of $S$ be the reduced power monoid associated…

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…

Let $S$ and $S'$ be numerical monoids. For a numerical monoid $T$, let $\mathcal P_{\mathrm{fin},0}(T)$ denote the power monoid of finite subsets of $T$ containing $0$. Isomorphism…

Let $S$ be a numerical monoid, and let $\mathcal P_{\mathrm{fin}}(S)$ denote its power monoid of finite nonempty subsets. For $A\in\mathcal P_{\mathrm{fin}}(S)$, let $\mathsf L(A)$…

Realizability conjecture. For every $n \in \mathbb{N}_{\ge 2}$ there exists a numerical monoid $N$ such that

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…

Set-of-length-sets conjecture. If

Length-set invariance conjecture. If $|G|,|G'|>3$ and

Let $\Gamma$ be a numerical monoid with least generator $n_1$, and let $\omega(n)$ denote its omega-function. Exact-period conjecture. For all sufficiently large $n$, the function…

Let $\Gamma = \langle n_1,n_2,n_3\rangle$ be a numerical monoid minimally generated by $n_1<n_2<n_3$, and let $\omega(n_i)$ denote the omega-value of $n_i$. The forbidden ordering…