10 problems

Integral-closedness criterion. If $\operatorname{Int}_K(A)$ is integrally closed, then $\operatorname{Int}_K(A)$ is Prüfer.

Let ${\mathbb Z}^{+}$ denote the positive integers, and for $n\in{\mathbb Z}^{+}$ define … where … Write $w_n(x)=w_n^{(1)}(x)$, let $(a,b)$ denote the greatest common divisor of…

For each integer $n\geq 1$, let $\mathcal{A}_n$ be the set defined in the paper, viewed as a subset of the algebraic integers $\overline{\mathbb{Z}}$. A subset is polynomially clos…

Let $R_k^B(n)$ denote the number of signed permutations of size $n$ whose burnt-pancake distance from the sorted stack is $k$. Summation identity conjecture. If $k,n\geq1$, then ……

Let $R$ be a Krull ring, and let $\operatorname{Int}(R)$ denote its ring of integer-valued polynomials. A PVMR is the corresponding Prüfer-v-multiplication ring notion for rings wi…

Let $d_k(x)$ and $s_k(x)$ be the two Delannoy-related polynomials considered in the paper. Integer-valued Delannoy-polynomial power conjecture. For all positive integers $m$ and…

Let $D$ be an integral domain. Non-plethory-domain conjecture. There exists an integral domain $D$ such that ${\operatorname{Int}}(D)$ is not an (idempotent) $D$-plethory. The prec…

Let $D$ be a Dedekind domain of characteristic zero with quotient field $K$. The Dedekind-domain containment conjecture. Every idempotent $D$-plethory is contained in $K[e]$, or, e…

Non-flatness conjecture. The domain $\operatorname{Int}(D)$ is not flat over $D$ for either of these choices of $D$; in particular, there exists a local, Noetherian, one-dimensiona…

Asymptotic cardinality conjecture. The minimal cardinality satisfies