16 problems

The $m$-Tamari lattice and the linear type $A$ $m$-Cambrian lattice are lattices associated with the same parameter $m$. Stump's interval-count conjecture. The $m$-Tamari lattice a…

Finite Coxeter Cambrian mutation conjecture. The Cambrian lattice $\operatorname{Camb}(Q)$ is mutable.

A Cambrian lattice is a lattice associated with a Coxeter group and its Coxeter element; a lattice is trim when it is both left modular and extremal. The Cambrian lattices in types…

Let $W$ be a finite reflection group containing $-1$, let $G$ be its Dynkin diagram, and let $\bar G$ be an orientation. Form the Coxeter element $c$ from the oriented diagram, ord…

Let $W$ be a finite reflection group containing $-1$, let $G$ be its Dynkin diagram, and let $\bar G$ be an orientation. Order the roots using their order as inversions in the word…

Ordovician lattice structure conjecture. The following hold:

The paper considers Fukaya–Seidel categories of certain quasi-homogeneous singularities and derived categories of lattices. Chapoton's conjecture. The Fukaya–Seidel categories of c…

Maximal-orbit conjecture. The set of elements of $\mathrm{Camb}_{c^{\times}}$ whose forward orbits under the pop-stack operator have size $h$ is

Extremal image-size conjecture. For every Coxeter element $c$ of $A_n$, we have

Thomas–Williams' biCambrian orbit conjecture. The orbit structure of rowmotion on $B(W,c)$ is the same as the orbit structure of rowmotion on $\mathcal J(P_W)$.

Let $\varepsilon$ be a signature, and let $I_\bullet \subseteq I'_\bullet$ and $J_\circ \subseteq J'_\circ$ be the indicated subsets. Write $\LatIJ$ for the…

Sublattice conjecture for c-Cambrian order interval posets. For every Coxeter element $c$, the set $\mathsf{COIP}(c)$ induces a sublattice of the weak order on $\mathcal{P}(\Phi)$.

Sublattice conjecture for c-Cambrian order element posets. For every Coxeter element $c$, the set $\mathsf{COEP}(c)$ induces a sublattice of the weak order on $\mathcal{P}(\Phi)$.

Snake-decomposition characterization. A $\Phi$-poset $\mathrel{\mathop{\rel}}\in\mathcal{P}(\Phi)$ is in $\mathsf{COEP}(c)$ if and only if it is in $\mathsf{COIP}(c)$ and every roo…

BiCambrian rowmotion conjecture. The orbit structure of rowmotion on the biCambrian lattices of these types coincides with the orbit structure of rowmotion on the corresponding min…

Forbidden-subgraph conjecture. The list in Proposition 1.6 is exhaustive: if $Gamma_{gamma}(W)$ contains none of the listed induced subgraphs, then $\mathcal{B}_{gamma}$ is distrib…