All Questions

Definition: A pure d-dimensional complex $\Delta$ is $k$-decomposable if either $\Delta$ is a $d-$simplex or $\Delta$ contains a face $F$ such that $\dim(F) \leq k$ both $\Delta \setminus F$ and $\...

Is there any result which gives us a relation between f-vector of simplicial complex and f-vector of nonfaces of a simplicial complex? Thank you

Let $\Delta$ be a simplicial complex on $[n]$ of dimension $d − 1.$ Let $0\le i\le d-1.$ One defines the pure i_th skeleton of $Δ$ to be the pure subcomplex $\Delta(i)$ of $\Delta$ whose facets are ...

Assume that $\Delta$ is a simplicial complex and $\Delta ^v$ is its Alexander dual. Let in addition $\Delta$ be pure, then what happens to betti-numbers of $I_{\Delta}$ or $I_{\Delta^v}$? Is there a ...

As the title suggests, I was wondering if anyone can point me to any examples in the literature to flag complexes that are shellable but not vertex decomposable. It is well-known that if a ...

Let $K$ bea field and $[n]=\{1,\ldots,n\}$ and $K[x]=K[x_1,\ldots,x_n]$. For $\sigma=\{i_1,\ldots,i_k\}\subseteq [n]$, denote $x_\sigma=x_{i_1}\cdots x_{i_k}=\prod_{i\in\sigma}x_i\in K[x]$. Let $\...