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.
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Acknowledgements
The authors would like to express their gratitude to the referees for dedicating their time, providing valuable feedback and guiding us in enhancing the paper through revisions in Section 2 and Section 4. The second author is supported by the Scientific and Technological Research Council of Turkey, International Postdoctoral Research Fellowship Program for Turkish Citizens TÜBİTAK-2219 (Project Number:1059B192201169). Additionally, the author gratefully thanks to the Department of Mathematical Sciences at Smith College for their warm hospitality.
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Fişekci, S., Sarıoğlan, S. Basis condition for generalized spline modules. J Algebr Comb 59, 359–369 (2024). https://doi.org/10.1007/s10801-023-01290-y
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DOI: https://doi.org/10.1007/s10801-023-01290-y