Abstract
In order to ensure existence of a de Boor algorithm (hence of a B-spline basis) in a given spline space with (n+1)-dimensional sections, it is important to be able to generate each spline by restriction to the diagonal of a symmetric function of n variables supposed to be pseudoaffine w.r. to each variable. We proved that a way to obtain these three properties (symmetry, n-pseudoaffinity, diagonal property) is to suppose the existence of blossoms on the set of admissible n-tuples, given that blossoms are defined in a geometric way by means of intersections of osculating flats. In the present paper, we examine the converse: do symmetry, n-pseudoaffinity, and diagonal property imply existence of blossoms?
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Communicated by J. Carnicer and J.M.Peña
I would like to make a present of this article to Mariano Gasca to celebrate many fruitful years of research and above all this, his 60th birthday. I would also like to thank him for his permanent cheerfulness and simplicity of nature which have made each encounter with him a pleasure to be looked forward to.
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Mazure, ML. Pseudoaffinity, de Boor algorithm, and blossoms. Adv Comput Math 26, 305–322 (2007). https://doi.org/10.1007/s10444-005-7450-0
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DOI: https://doi.org/10.1007/s10444-005-7450-0