All Questions

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

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 ...

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 $\...