3 problems

Let $\Delta$ be a $(d-1)$-dimensional balanced normal pseudomanifold, with $d\geq 4$, and suppose that $f_0(\Delta)=kd$ for an integer $k\geq 2$. Let $\mathbb{F}[\Delta]$ denote it…

Let a balanced normal pseudomanifold mean a balanced normal pseudomanifold, and let its Stanley–Reisner ring be denoted by $\mathbb{F}[\Delta]$. For a cross-polytopal stacked spher…

Let $\Delta$ be a balanced normal pseudomanifold of dimension $d-1\geq 3$. Klee–Novik's balanced lower bound conjecture. … This extends the balanced Lower Bound Theorem by includin…