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Module Basis for Generalized Spline Modules
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Let G = (V,E) be a graph of order n. Let R be a commutative ring and I denote the set of all ideals of R. Let ? : E ? I be an edge labeling. A generalized spline of (G, ?) is a vertex labeling F : V ? R such that for each edge uv, F(u) ? F(v) ? ?(uv). The set R(G,) of all generalized splines of (G, ?) is an R-module. In this paper we determine conditions for a subset of R(G,?) to form a basis of R(G,?) for some classes of graphs.
Keywords
Generalized Spline Modules, Dutch Windmill Graph, Isomorphic Graphs.
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- S. Altinok and S. Sarioglan, Basis criteria for generalized spline modules via determinant, Discrete Math., 344 (2021), 112223.
- S. Altinok and S. Sarioglan, Flow-up bases for generalized spline modules on arbitrary graphs, J. Algebra Appl. 20(10), 2150180 (2021).
- M. Atiyah and I. MacDonald, Introduction To Commutative Algebra, Addison-Wesley, Reading, Mass. 1969.
- L. J. Billera and L. L. Rose, A dimension series for multivariate splines, Discrete Comput. Geom., 6(2) (1991), 107–128.
- N. Bowden and J. Tymoczko, Splines mod m, ArXiv e-prints (2015).
- J. P. Dalbec and H. Schenck, On a conjecture of rose, J. Pure Appl. Algebra, 165 (2)(2001), 151–154.
- M. R. DiPasquale, Shellability and freeness of continuous splines, J. Pure Appl. Algebra, 216(11) (2012), 2519-2523.
- E. Gjoni, Basis criteria for n-cycle integer splines, Bard College Senior Projects Spring 2015, Bard College, NY 2015.
- E. Estrada, When local and global clustering of networks diverge, Linear Algebra Appl., 488 (2016), 249–263.
- S. Gilbert, S. Polster and J. Tymoczko, Generalized splines on arbitrary graphs, Pac. J. Appl. Math., 281 (2016), 333–364
- R. Haas, Module and vector space bases for spline spaces, J. Approx. Theory, 65(1) (1991), 73-89.
- M. Handschy, J. Melnick and S. Reinders, Integer Generalized Splines on Cycles, arXiv:Combinatrics (2014).
- F. Harary. Graph Theory, Addison-Wesley, Reading, MA. 1984.
- E. R. Mahdavi, Integer generalized splines on the diamond graph, Bard College Senior Projects Spring 2016, Bard College, NY. 2016.
- L. L. Rose, Graphs, syzygies and multivariate splines, Discrete Comput. Geom., 32(4) (2004), 623-637.
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