12 problems

Quadratic generation conjecture. The defining ideal $I_{{\mathcal R}_K(L)}$ is generated by quadrics if and only if at most one interval is $D_{2^{2}\cdot 3^{2}}$.

Let $\mathcal{L}$ be a locally-finite distributive lattice, and let $\mathcal{P}$ be its set of prime filters. Let $\mathcal{I}$ be the lattice of ideals of $\mathcal{P}$. A lattic…

Let $\textbf m$ and $\textbf n$ denote chains indexed by the positive integers $m$ and $n$, and let $\textbf m\times\textbf n$ be their product lattice. A lattice is Schur positive…

For positive integers $m$ and $n$, let $\mathbf m\times\mathbf n$ be the product of two chains, and let $\operatorname{inc}(\mathbf m\times\mathbf n)$ denote its incomparability gr…

For positive integers $n_1,\ldots,n_r$, let $\mathbf{n_i}$ denote a chain of length $n_i$, and let a lattice be nice when every stable-partition type dominates only types that are…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its distributive lattice of lower order ideals. For a linear extension of $F(\beta)$, form the corresponding lexicographic chain dec…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its distributive lattice of lower order ideals, with rank sequence governed by the alternatives in Theorem heavy. A saturated chain…

Let $F(\beta)$ be a fence and let $L(\beta)$ be the distributive lattice of lower order ideals of $F(\beta)$. Its rank sequence is $r(\beta):r_0,r_1,\ldots,r_n$, where $r_k$ is the…

Dual Ore conjecture. Every distributive interval $[H,G]$ of finite groups is linearly primitive; equivalently, there exists an irreducible complex representation $V$ of $G$ such th…

Let $Y$ be a poset, let $L(Y)$ be the distributive lattice of all finite ideals of $Y$, and let $\Gamma$ be the Hasse diagram of $L(Y)$. Consider the space of all minimal infinite…

Minuscule mCDE conjecture. The distributive lattice $J(P)$ is mCDE.

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…