Basis condition for generalized spline modules

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Fişekci S., SARIOĞLAN S.

Journal of Algebraic Combinatorics, cilt.59, sa.2, ss.359-369, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s10801-023-01290-y
  • Dergi Adı: Journal of Algebraic Combinatorics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.359-369
  • Anahtar Kelimeler: 05C78, 15A15, Basis, Generalized spline, Module
  • TED Üniversitesi Adresli: Evet

Özet

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.