An Upper Bound for the Symmetric Tensor Rank of a Low Degree Polynomial in a Large Number of Variables. (18th February 2013)

• Record Type: Journal Article
• Authors: Ballico, E.
• Other Names: Planat Michel Academic Editor.
• Is Part Of: Geometry. Volume 2013(2013)
• Publication Date: 2013-02-18
• Subjects: Geometry -- Periodicals; Geometry; Periodicals; 516
• DOI: 10.1155/2013/715907
• Languages: English
• ISSNs: 2314-422X

Abstract

Abstract : Fix integers m ≥ 5 and d ≥ 3 . Let f be a degree d homogeneous polynomial in m + 1 variables. Here, we prove that f is the sum of at most d · ⌈ ( m + d m ) / ( m + 1 ) ⌉ d -powers of linear forms (of course, this inequality is nontrivial only if m ≫ d .)