6 problems

Let $(G,\beta)$ be an edge-labeled graph over a GCD domain $R$, and let $F_1,F_2,\ldots,F_n\in\hat{R}_G$ be splines. The determinant of these splines is denoted by…

Let $(G,A)$ be an edge-labeled graph, where $A=\{a_1,\ldots,a_m\}$ is an arbitrary set of elements of a GCD domain $R$. Let $l_1,\ldots,l_n$ have the same theoretical form, in term…

Let $R$ be a GCD domain, let $G$ be an edge-labeled graph with $n$ vertices, and let $R_G$ be its generalized spline module. Let $Q$ be maximal with respect to dividing the determi…

Let $R$ be a GCD domain and let $R_G$ be the generalized spline module of an edge-labeled graph. Suppose a determinant divisibility result is known for $n$-element subsets of $R_G$…

Let $R$ be the GCD domain underlying the generalized spline module, let $(G,\alpha)$ be an edge-labeled graph with $n$ vertices, and let $Q_G$ be the graph-dependent element define…

Let $(D_{3,3},\alpha)$ be the edge-labeled diamond graph with edge labels $l_1,\ldots,l_5$, and let $\mathbb{Z}_{(D_{3,3},\alpha)}$ denote its integer generalized spline module. De…