2 problems

Let $d$ and $n$ be positive integers. A normal pure $(d-1)$-complex is a pure simplicial complex in which the link of every face of codimension at least two is connected. Its diame…

Let $\mathcal{A}$ be a simple arrangement of $n$ hyperplanes in dimension $d$. If $P_1,\ldots,P_I$ are its bounded cells, where $I={n-1\choose d}$, let … where $\delta(P_i)$ is the…