Paper Info
Title
Splines on the Alfeld split of a simplex and type A root systems.
Abstract
Alfeld (1984) introduced a tetrahedral analog AS(Δ3) of the Clough–Tocher split of a triangle. A formula for the dimension of the spline space Ckr(AS(Δn)) is conjectured in Foucart and Sorokina (2013). We prove that the graded module of Cr-splines on the cone over AS(Δn) is isomorphic to the module Dr+1(An) of multiderivations on the type An Coxeter arrangement. A theorem of Terao shows that the module of multiderivations of a Coxeter arrangement is free and gives an explicit basis. As a consequence the conjectured formula holds.
Year
DOI
Venue
2014
10.1016/j.jat.2014.02.005
Journal of Approximation Theory
Keywords
DocType
Volume
Spline,Hyperplane arrangement,Dimension formula
Journal
182
ISSN
Citations 
PageRank 
0021-9045
1
0.37
References 
Authors
2
1
Name
Order
Citations
PageRank
Hal Schenck1304.50