Graphs Admitting Only Constant Splines

Authors

Katie Anders, University of Texas at Tyler
Alissa S. Crans, Loyola Marymount University
Briana Foster-Greenwood, Cal Poly Pomona
Blake Mellor, Loyola Marymount University
Julianna Tymoczko, Smith CollegeFollow

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.

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Anders, Katie; Crans, Alissa S.; Foster-Greenwood, Briana; Mellor, Blake; and Tymoczko, Julianna, "Graphs Admitting Only Constant Splines" (2020). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/101