2 problems

Strong polarization conjecture. The inequality above holds for every set of $n$ vectors in $\mathbb{S}^{d-1}$.

Let $R=\mathbb{K}[X_1,\ldots,X_n]$ be a polynomial ring, let $I\subset R$ be a monomial ideal, and let $I^p\subset R^p$ be its polarization, where $R^p$ is the polynomial ring in w…