6 papers
Generalized graph splines and the Universal Difference Property
Selma Altınok, Katie Anders, Daniel Arreola +4
We study the generalized graph splines introduced by Gilbert, Tymoczko, and Viel and focus on an attribute known as the Universal Difference Property (UDP). We prove that paths, tr…
Minimum Generating Sets for Complete Graphs
Selma Altınok, Gökçen Dilaver
Let be a graph whose edges are labeled by ideals of a commutative ring with identity. Such a graph is called an edge-labeled graph over . A generalized spline is a verte…
Multivariate generalized splines and syzygies on graphs
Selma Altınok, Samet Sarıoğlan
Given a graph whose edges are labeled by ideals of a commutative ring with identity, a generalized spline is a vertex labeling of by the elements of so that the dif…
Basis Criteria for Generalized Spline Modules via Determinant
Selma Altinok, Samet Sarioglan
Given a graph whose edges are labeled by ideals of a commutative ring R with identity, a generalized spline is a vertex labeling by the elements of R such that the difference of th…
Flow-up Bases for Generalized Spline Modules on Arbitrary Graphs
Selma Altinok, Samet Sarioglan
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…
Fano 3-folds, K3 surfaces and graded rings
Selma Altınok, Gavin Brown, Miles Reid
Explicit birational geometry of 3-folds represents a second phase of Mori theory, going beyond the foundational work of the 1980s. This paper is a tutorial and colloquial introduct…