Graphs admitting only constant splines
Combinatorics
2020-02-12 v2
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.
Keywords
Cite
@article{arxiv.1807.11515,
title = {Graphs admitting only constant splines},
author = {Katie Anders and Alissa Crans and Briana Foster-Greenwood and Blake Mellor and Julianna Tymoczko},
journal= {arXiv preprint arXiv:1807.11515},
year = {2020}
}
Comments
19 pages; this version has substantial revisions, and is the version accepted by the Pacific Journal of Mathematics