2 problems

Strong structure conjecture. There exist possibly identical collections $\mathcal{C}_\mu$ and $\overline{\mathcal{C}}_\mu$ of Dyck partitions satisfying conditions (1)--(9): the tw…

Conjectured chain decomposition. There exists a sequence of Dyck partitions $\{\gamma_{\lambda,i}:i\in\mathbb{Z}_{>0}\}$ with strictly increasing sizes satisfying all five stated c…