2 problems

Let $X_{n-2,q}$ be the spherical building of dimension $n-2$ and thickness $q+1$. For $0\leq i\leq n-2$, let $d_i$ and $\delta_i$ denote the coboundary and boundary operators at le…

Let $G$ be a $d$-regular triangle-free graph with $n$ vertices, where … Under the notion in Chapman (2018), let … Here $\operatorname{Aux}(\Gamma)$ denotes the auxiliary complex as…