Seeking for the Maximum Symmetric Rank

Abstract

We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order. After a general discussion on the interplay between symmetric tensors, polynomials and divided powers, we introduce the technical environment and the methods that have been set up in recent times to find new lower and upper bounds.

Keywords

• symmetric tensor
• tensor rank
• Waring rank
• power sum