Mathematics in Computer Science

, Volume 8, Issue 2, pp 157–174 | Cite as

Bounds on the Dimension of Trivariate Spline Spaces: A Homological Approach

Article

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 of 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 Fröberg–Iarrobino conjecture, and the weak Lefschetz property.

Keywords

Triangulations Splines Dimension Tetrahedral partition Ideals of powers of linear forms Fröberg’s conjecture 

Mathematics Subject Classification

13 14 68 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Inria Sophia Antipolis MéditerranéeSophia AntipolisFrance
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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