Holographic Entropy Inequalities and the Topology of Entanglement Wedge Nesting

We prove two new infinite families of holographic entropy inequalities. A key tool is a graphical arrangement of terms of inequalities, which is based on entanglement wedge nesting (EWN). It associates the inequalities with tessellations of the torus and the projective plane, which reflect a certain topological aspect of EWN. The inequalities prove a prior conjecture about the structure of the holographic entropy cone and show an interesting interplay with differential entropy.