Graphs admitting only constant splines

Authors

Alissa Crans, Loyola Marymount UniversityFollow
Blake Mellor, Loyola Marymount UniversityFollow

Document Type

Article

Publication Date

2020

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.

Original Publication Citation

Anders, Katie, et al. “Graphs Admitting Only Constant Splines.” Pacific Journal of Mathematics, vol. 304, no. 2, Jan. 2020, p. 385-400.

Digital Commons @ LMU & LLS Citation

Crans, Alissa and Mellor, Blake, "Graphs admitting only constant splines" (2020). Mathematics, Statistics and Data Science Faculty Works. 168.
https://digitalcommons.lmu.edu/math_fac/168