Gaps in the Pairs (Border Rank, Symmetric Rank) for Symmetric Tensors - Ballico, E. (Sarajevo Journal of Mathematics, 2024)
Fix integers $m \ge 2$, $s\ge 5$ and $d\ge 2s+2$. Here we describe the possible symmetric tensor ranks $\le 2d+s-7$ of all symmetric tensors (or homogeneous degree $d$ polynomials) in $m+1$ variables with border rank $s$. 2010 Mathematics Subject Classification. 14N05, 15A69, 15A21