Partially symmetric tensor rank: the description of the non-uniqueness case for low rank. Issue 3 (4th March 2018) - Ballico, E.
Abstract : We study the partially symmetric tensors T with low rank whose rank is not achieved by a unique set when the rank has an upper bound like, where is the minimum of the entries of the multidegree of T . For the proof, we use the Hilbert function of finite subsets of a product of projective spaces with respect to a Segre–Veronese embedding.