6 problems

Let the reduced finitary power monoid of the additive group $(\mathbb{Z},+)$ be the quotient of the finitary power monoid by translation equivalence, and let $X\mapsto -X$ denote t…

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 $H$ 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…

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 $S$ 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 $\mathsf L(A)$…