6 problems

Let $\Delta$ be a boolean complex with an action by a group $G$ of automorphisms, and let $\operatorname{Sd}\Delta$ be its barycentric subdivision, with the induced $G$-action. Let…

Let $\Delta$ be a boolean complex, let $\operatorname{Sd}\Delta$ be its barycentric subdivision, and let $\Bbbk[\Delta]$ and $\Bbbk[\operatorname{Sd}\Delta]$ be their face rings. L…

Let $\Delta$ be a simplicial complex, and let $\mathcal{L}(\Delta)$ be the induced subcomplex of the barycentric subdivision $\mathcal{B}(\Delta)$ on the vertices $u_\sigma$ for wh…

Let $\Delta$ be a simplicial complex. For an integer $i\geq -1$, let $\mathcal{L}_{i}(\Delta)$ be the induced subcomplex of the barycentric subdivision $\mathcal{B}(\Delta)$ on the…

For each relevant integer $n$, let $d_n$ denote the dimension parameter associated with the poset $P_n$, and let $\alpha_n$ be defined by … Here $\gg$ denotes a lower bound up to a…

Let $K$ be a Cohen–Macaulay simplicial complex, and let $\operatorname{sd}(K)$ denote its barycentric subdivision. The Kubitzke–Nevo conjecture. The simplicial complex…