2000 character limit reached
Determinantal Conditions for Modules of Generalized Splines (2208.13062v1)
Published 27 Aug 2022 in math.AC and math.CO
Abstract: Generalized splines on a graph $G$ with edge labels in a commutative ring $R$ are vertex labelings such that if two vertices share an edge in $G$, the difference between the vertex labels lies in the ideal generated by the edge label. When $R$ is an integral domain, the set of all such splines is a finitely generated $R$-module $R_G$ of rank $n$, the number of vertices of $G$. We find determinantal conditions on subsets of $R_G$ that determine whether $R_G$ is a free module, and if so, whether a so called "flow-up class basis" exists.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.