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