3 problems

Shellability conjecture. The intervals in the level Eulerian poset from Section are shellable, and hence their order complexes are homeomorphic to spheres.

Let $P$ be a graded Eulerian poset, and let $\Phi_P$ denote its cd-index. A poset is Gorenstein when it has the homology type of a sphere; in the source this is described as $P$ tr…

Let $P$ be a finite Eulerian Sheffer poset of rank $5$ satisfying $B(3)=6$ and $D(3)=10$. Nonexistence conjecture. There is no poset $P$ with these conditions. This is one of the r…