4 problems

Let $\mathrm{Fw}_n$ denote the boundary framework, let $L_r(n)$ be the vertices of local simplex dimension $r$, and let $(n)$ and $(1^n)$ be the two antenna vertices. Low-dimension…

Let $L_r(n)$ be the vertices of local simplex dimension $r$ in the partition graph, let $\tau(r)$ be the least $n$ for which $L_r(n)$ is nonempty, and let…

Let $G_n$ be the partition graph, let $K_n$ be its clique complex, let $L_r(n)$ denote the vertices of local simplex dimension $r$, let $\Delta(n)$ be the maximal local simplex dim…

Let $G_n$ be the partition graph on the partitions associated with the parameter $n$, and consider its simplicial thick zones, including the tetrahedral and higher-order regions. T…