Graphs admitting only constant splines
arXiv:1807.11515 · doi:10.2140/pjm.2020.304.385
Abstract
We study {\em generalized graph splines,} introduced by Gilbert, Viel, and the last author. For a large class of rings, we characterize the graphs that only admit constant splines. To do this, we prove that if a graph has a particular type of cutset (e.g., a bridge), then the space of splines naturally decomposes as a certain direct sum of submodules. As an application, we use these results to describe splines on a triangulation studied by Zhou and Lai, but over a different ring than they used.
19 pages; this version has substantial revisions, and is the version accepted by the Pacific Journal of Mathematics
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