20 problems

Minuscule doppelgänger mCDE conjecture. The lattices $J(P)$ and $J(Q)$ are both mCDE, with edge densities satisfying

Let $(W,S)$ be a finite Coxeter group, let $\boldsymbol{\operatorname{Sort}}_\omega(W)$ be a distributive sorting order, and let $J=S\setminus\{s\}$ for some $s\in S$. Write $W_J$…

A distributive sorting order is a sorting order that is a distributive lattice, and types $B$, $C$, and $D$ refer to the corresponding finite Coxeter types. Completeness conjecture…

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…

Nation–Picketing's conjecture. Having a distributive skeleton should be sufficient for $L$ to be type-1 representable.

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…

A chip configuration on the one-dimensional grid is ordered by reachability under chip-firing; the resulting poset is called the configuration poset. A lattice is distributive if i…

Let $\alpha=(a,b,\ldots)$ be a composition. The fence $F(\alpha)$ is the poset whose covering relations begin … Let $L(\alpha)$ be the distributive lattice of all lower order ideal…

Reiner–Tenner–Yong's conjecture. The distributive lattice $J(T_{k,n})$ is CDE.

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…

A minuscule poset is a poset arising in the representation theory of a semisimple Lie algebra; for a poset $P$, let $J(P)$ denote its associated distributive lattice. The property…

Geissinger's conjecture. The vertices of $\mathrm{Val}(\mathcal{J})$ are exactly the valuations whose values lie in $\{0,1\}$.

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…

Let $L$ be a distributive lattice, and let condition (b) in Theorem be the condition stated there for the levelness of the Hibi ring associated with $L$. Levelness conjecture. Cond…

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…

The singular-locus conjecture.