Flow-up bases for generalized spline modules on arbitrary graphs.

Altınok, Selma; Sarıoğlan, Samet

Let R be a commutative ring with identity. An edge labeled graph is a graph with edges labeled by ideals of R. A generalized spline over an edge labeled graph is a vertex labeling by elements of R , such that the labels of any two adjacent vertices agree modulo the label associated to the edge connecting them. The set of generalized splines forms a subring and module over R. Such a module is called a generalized spline module. We show the existence of a flow-up basis for the generalized spline module on an edge labeled graph over a principal ideal domain by using a new method based on trails of the graph. We also give an algorithm to determine flow-up bases on arbitrary ordered cycles over any principal ideal domain.

GRAPH labelings; COMMUTATIVE rings; ALGORITHMS; SPLINE theory; GRAPH theory

Journal of Algebra & Its Applications, 2021, Vol 20, Issue 10, p1

0219-4988

Academic Journal

10.1142/S0219498821501802