3 problems

Let $P$ be a Cohen–Macaulay CW-poset or a Gorenstein poset of rank $n$, let $\mathcal A_n$ be the indexing family for its flag $f$-vector coefficients, and let $\alpha_S(P)$ denote…

Let $P$ be an $(n-1)$-dimensional regular CW-sphere, or more generally a Gorenstein poset of rank $n+1$. Write its homogeneous cd-index as … where $w$ ranges over cd-monomials of d…

Flag $h$-vector minimization conjecture. If $L$ is Cohen–Macaulay over $\mathbf{k}$ and $\mu_L(\hat{0},\hat{1})\ne 0$, then