A general method computes dimensions of spline spaces on arbitrary rectilinear partitions by reducing the problem to rank of constructible conformality matrices, and proves Schumaker's lower bound is attained for partitions with disjoint truncated l-edges.
Algebraic methods to study the dimension of super- smooth spline spaces
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Dimension Calculation for Spline Spaces over Rectilinear Partitions via Smoothing Cofactor Method
A general method computes dimensions of spline spaces on arbitrary rectilinear partitions by reducing the problem to rank of constructible conformality matrices, and proves Schumaker's lower bound is attained for partitions with disjoint truncated l-edges.