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Graphs admitting only
constant splines
Katie Anders, Alissa S. Crans, Briana Foster-Greenwood, Blake Mellor and Julianna Tymoczko |
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Vol. 304 (2020), No. 2, 385–400
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Abstract |
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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
splines, generalized graph splines
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Mathematical Subject Classification 2010
Primary: 05C25, 05C78, 05E15
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Milestones
Received: 8 August 2018
Revised: 25 July 2019
Accepted: 2 October 2019
Published: 12 February 2020
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Authors |
| Katie Anders | |
| Department of Mathematics University of Texas at Tyler Tyler, TX United States |
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| Alissa S. Crans | |
| Department of Mathematics Loyola Marymount University Los Angeles, CA United States |
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| Briana Foster-Greenwood | |
| Department of Mathematics and
Statistics California State Polytechnic University Pomona, CA United States |
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| Blake Mellor | |
| Department of Mathematics Loyola Marymount University Los Angeles, CA United States |
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| Julianna Tymoczko | |
| Department of Mathematics and
Statistics Smith College Northampton, MA United States |
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