Missing faces of neighborly and nearly neighborly polytopes and spheres

Isabella Novik, Hailun Zheng

For a $(d-1)$-dimensional simplicial complex $\Delta$ and $1\le i\le d$, let $f_{i-1}$ be the number of $(i-1)$-faces of $\Delta$ and $m_i$ be the number of missing $i$-faces of $\Delta$. In th…