Establishes equivalence between Hankel flat extension and multiplication tensor completion for cactus rank in Artinian Gorenstein algebras, plus reduction of basis shapes via Borel-fixed staircases.
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Gives explicit characterization and algorithm for Waring decompositions of symmetric tensors on rational varieties under a technical assumption, generalizing Hankel tensors, plus new quadrature bounds on rational curves.
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Hankel and Multiplication Tensor Completions for Cactus Rank
Establishes equivalence between Hankel flat extension and multiplication tensor completion for cactus rank in Artinian Gorenstein algebras, plus reduction of basis shapes via Borel-fixed staircases.