Pseudoaffinity, de Boor algorithm, and blossoms (Q878093)

Several theorems dealing with the question if symmetry, \(n\)-pseudoaffinity and diagonal property imply the existence of blossoms are given. The main result states, under assumption of ability to associate with any spline a function of \(n\)-variables, defined on the set of admissible \(n\)-tuples, that is symmetric, \(n\)-pseudoaffine, and that has diagonal and differentiability property, that blossoms exist in the spline space defined on the set of admissible \(n\)-tuples.