5 problems

An increasing tableau of shape $\lambda$ with entries in $[q]\coloneqq\{1,\ldots,q\}$ is a filling of the Young diagram of $\lambda$ with elements of $[q]$ whose rows and columns a…

Thomas–Williams' conjecture. The operator

Let $F(\beta)$ be a fence and let $L(\beta)$ be its lattice of lower order ideals. Suppose $k\ge 2$ and $\beta=(k-1,k,k,\ldots,k,k-1)$ has an odd number of parts. Under rowmotion o…

Fix positive integers $a,b,c$ and let $\mathsf{B}_{a,b,c}={\bf a}\times{\bf b}\times{\bf c}$ be the product of three chains. Let $J(\mathsf{B}_{a,b,c})$ denote its order ideals, an…

Let $\Delta$ be a reduced irreducible root system with positive roots $\Delta^+$, simple roots $\Pi$, Coxeter number $h$, and reverse operator $\mathfrak X_0$ on the antichains of…