The symmetric determinantal complexity $\sdc(f)$ of a polynomial $f$ is the
least $m$ such that $f=\Det(M)$ for an $m\times m$ symmetric matrix $M$ of
affine-linear forms. We prove, over $\CC$, that
\[
\sdc\!\left(\sum_{i=1}^n x_i^n\right)
\ge \left(\frac{1}{2e}-o(1)\right)n^2 .
\]
The result is a symmetric companion to the author's non-symmetric ... more >>>