Paper Info
Title
Bounds on the Dimension of Trivariate Spline Spaces: A Homological Approach.
Abstract
We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by applying homological techniques. We give an insight into different ways of approaching this problem by exploring its connections with the Hilbert series of ideals generated by powers of linear forms, fat points, the so-called Fr\"oberg-Iarrobino conjecture, and the weak Lefschetz property.
Year
DOI
Venue
2014
10.1007/s11786-014-0187-8
Mathematics in Computer Science
Keywords
DocType
Volume
Triangulations, Splines, Dimension, Tetrahedral partition, Ideals of powers of linear forms, Froberg's conjecture
Journal
8
Issue
ISSN
Citations 
2
1661-8270
0
PageRank 
References 
Authors
0.34
2
2
Name
Order
Citations
PageRank
Bernard Mourrain11074113.70
Nelly Villamizar2132.72