Document Type
Article
Publication Date
1-1-2020
Publication Title
Pacific Journal of Mathematics
Abstract
We study generalized graph splines, introduced by Gilbert, Tymoczko, and Viel (2016). 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
Generalized graph splines, Splines
Volume
304
Issue
2
First Page
385
Last Page
400
DOI
10.2140/pjm.2020.304.385
ISSN
00308730
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.
Recommended Citation
Anders, Katie; Crans, Alissa S.; Foster-Greenwood, Briana; Mellor, Blake; and Tymoczko, Julianna, "Graphs Admitting Only Constant Splines" (2020). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/101
Comments
Peer reviewed accepted manuscript.