4 problems

Rotational $\Lambda\Sigma=\Delta$ conjecture.

The $q,t$-dihedral sieving conjecture. For every $\mathbf{F}\in\operatorname{Dih}_{n+2}$ and $\sigma\in\mathfrak{S}_n$,

The $\Lambda\Sigma=\Delta$ conjecture. We have $\Lambda\Sigma=\Delta$.

Let $\Gamma^{(m)}$ be the generalized cluster complex, and let cluster parking functions be faces of $\Gamma^{(m)}$ equipped with additional structure, essentially a labeling by a…