For a planar simplicial complex , Schumaker proves in  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  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. 359–367DOI 10.4171/JCA/43