3 problems

The modular-lattice integrality conjecture. Every modular lattice is integral.

Let $\Delta$ be a triangulation of a sphere, and let $P_\Delta$ be its face poset, consisting of all faces of $\Delta$, including $\emptyset$, ordered by inclusion. Recall that…

Let $P$ be a finite poset that is a disjoint union of chains. Write ${\mathcal J}(P)$ for the poset of order ideals of $P$, and let $K[\mathcal O(P)]$, $K[\mathcal C(P^)]$, and…