A new bound for smooth spline spaces

  • Hal Schenck

    Auburn University, USA
  • Mike Stillman

    Cornell University, Ithaca, USA
  • Beihui Yuan

    Cornell University, Ithaca, USA
A new bound for smooth spline spaces cover

A subscription is required to access this article.

Abstract

For a planar simplicial complex , Schumaker proves in [22] that a lower bound on the dimension of the space of planar splines of smoothness and degree on is given by a polynomial , and Alfeld–Schumaker show in [2] that gives the correct dimension when . Examples due to Morgan–Scott, Tohaneanu, and Yuan show that the equality can fail for . In this note we prove that the equality cannot hold in general for .

Cite this article

Hal Schenck, Mike Stillman, Beihui Yuan, A new bound for smooth spline spaces. J. Comb. Algebra 4 (2020), no. 4, pp. 359–367

DOI 10.4171/JCA/43