The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, date it has only been possible completely characterize HEC for at most $n=5$ parties. For larger $n$, our knowledge falls short incomplete: almost nothing is known about extremal elements. Here, we introduce a symmetrizati...

Let’s first see how primitive covers were inadequate. Recall that a function class G is a primitive cover for a function class F at scale > 0 over some set S if: • G ⊆ F , • |G| <∞, and • for every f ∈ F there exists g ∈ G with supx∈S |g(x)− f(x)| ≤ . Last class, we gave a generalization bound for classes with primitive covers (basically, primitive covers give discretizations, and then we apply...

Given a multi-variable polynomial, there is an associated divided symmetrization (in particular turning it into a symmetric function). Postinkov has found the volume of a permutohedron as a divided symmetrization (DS) of the power of a certain linear form. The main task in this paper is to exhibit and prove closed form DS-formulas for a variety of polynomials. We hope the results to be valuable...