11 problems

Geode conjecture. With $k-2$ leading zeros, $G[0,\dots,m_k]$ is a two-parameter Fuss–Catalan number.

Place $n-2$ points labeled $0,1,\ldots,n-3$ in increasing order on the real line, and let $H(x)$ be the function in the global Schwinger formula for $A^{\phi^p}_n$. For a non-cross…

Let $P_d(n)$ denote the number of $(n,n+1)$-core partitions whose parts are all divisible by $d$. Write … where $0\leq r<d$. Amdeberhan's conjecture. The number $P_d(n)$ is … The t…

Let $W$ be a crystallographic reflection group, let $\mathsf{Shi}^{(m)}(W)$ be the extended Shi arrangement, and let $\operatorname{coh}(R)$ be the coheight of a positive region…

Let $W$ be a well-generated complex reflection group of rank $\ell$, acting on $\mathbb{C}[V\oplus V^*]$. Let $d_i$ and $d_i^*$ be the invariant and codegrees appearing in the sour…

Let $W$ be a well-generated complex reflection group, let $D\!R^{(m)}(W)$ be the space of generalized diagonal coinvariants, and let $\mathbf{e}_{\epsilon}$ denote the idempotent p…

Let $\mathcal{D}_n^{(m)}$ be the set of $m$-Dyck paths of semilength $n$, let $\operatorname{area}(D)$ be the area statistic, and let $\operatorname{bounce}(D)$ be the bounce stati…

Let $W$ be a well-generated complex reflection group, let $m$ be a positive integer, and let $\operatorname{Cat}^{(m)}(W;q,t)$ and $\operatorname{Cat}^{(m)}(W)$ denote the generali…

Let $W$ be a crystallographic reflection group, and let $\operatorname{Cat}^{(m)}(W,q)$ be the combinatorial $q$-Fuss-Catalan number obtained by summing $q^{\operatorname{coh}(R)}$…

Let $W$ be a well-generated complex reflection group of rank $l$, with fundamental-invariant degrees $d_1\leq\cdots\leq d_l$, Coxeter number $h=d_l$, and $N:=\sum_{i=1}^l(d_i-1)$.…

Let $W$ be a well-generated complex reflection group. The $q,t$-Fuss-Catalan number is defined by … where $M^{(m)}$ is the associated $W$-module, so that…