2 problems

Let $\tau$ be a preorder of size $n$, let $P_\tau$ be its lattice-point poset, and let $\overline M_{P_\tau}$ be the transmuted $M$-triangle. Transmuted M-triangle duality conjectu…

Lattice-realization conjecture. There exists a finite graded lattice $L_\tau$ of rank $n$ such that