5 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…

Let $s$ and $t$ be coprime positive integers, and let $\lambda$ range over the $(s,t)$-core partitions. Write $n(\lambda)$ for the number of parts of $\lambda$ and $m(\lambda)$ for…

Let $(W,S)$ be a Coxeter system with $W\in\{A_n,B_n,H_3,I_2(m)\}$, and let $J\subseteq S$. The sets $\operatorname{Align}(W^J,c)$, $\operatorname{NC}(W^J,c)$,…

Let $c(p,q,n)$ denote the number of planted trees on $n$ vertices with $p$ crucial vertices and root having $q$ children. For fixed $n$, let … The Speyer conjecture. The polynomial…

Let $W$ be a Weyl group, let $R^+$ be its positive roots ordered by $\alpha\prec\beta$ when $\beta-\alpha$ is a positive sum of simple roots, and let $J(R^+,\prec)$ be the set of u…