Basis condition for generalized spline modules

Seher Fişekci; Samet Sarıoğlan

Basis condition for generalized spline modules

Commutative Algebra 2023-01-31 v1

Authors: Seher Fişekci , Samet Sarıoğlan

Abstract

A generalized spline on an edge labeled graph $(G,\alpha)$ is defined as a vertex labeling, such that the difference of labels on adjacent vertices lies in the ideal generated by the edge label. We study generalized splines over greatest common divisor domains and present a determinantal basis condition for generalized spline modules on arbitrary graphs. The main result of the paper answers a conjecture that appeared in several papers.

Keywords

spline theory graph theory generalization theorems

Cite

@article{arxiv.2301.12529,
  title  = {Basis condition for generalized spline modules},
  author = {Seher Fişekci and Samet Sarıoğlan},
  journal= {arXiv preprint arXiv:2301.12529},
  year   = {2023}
}