Basis condition for generalized spline modules

Creative Commons License

Fişekci S., SARIOĞLAN S.

Journal of Algebraic Combinatorics, vol.59, no.2, pp.359-369, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1007/s10801-023-01290-y
  • Journal Name: Journal of Algebraic Combinatorics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.359-369
  • Keywords: 05C78, 15A15, Basis, Generalized spline, Module
  • TED University Affiliated: Yes

Abstract

A generalized spline on an edge-labeled graph (G,α) 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.