5 problems

Let $I_n$ be the ideal generated by alternating polynomials in $R=\mathbb{C}[x_1,y_1,\ldots,x_n,y_n]$, and let $q$ and $t$ record the two gradings. Write $s_1^n$ for the $n$-fold p…

Let $R_{n,k}(q,t)$ be the $(q,t)$-Schröder polynomial obtained by weighting little Schröder paths with the statistics defined above, and let $[m]_q$ and $[m]!_q$ denote the $q$-int…

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 $(W,S)$ 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 $W$ 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…