13 problems

Generalised Delta square conjecture, valley version.

Euler-number specialization conjecture.

The $q,t$-dihedral sieving conjecture. For every $\mathbf{F}\in\operatorname{Dih}_{n+2}$ and $\sigma\in\mathfrak{S}_n$,

Loehr–Warrington conjecture. Loehr and Warrington conjectured that

Let $m,n\in\mathbb{N}$, let $\mathsf{LPP}(m+1,n+1)$ be the set of labelled parallelogram polyominoes of the indicated dimensions, and let $\mathsf{area}(P)$, $\mathsf{pmaj}(P)$ and…

Let $m,n,k$ be in the range for which $\mathsf{PLD}(m,n)^{\ast k}$ is defined, and let $\mathsf{pmaj}(D)$ denote the proposed partial-major-index statistic on a partially labelled…

Modified Delta square conjecture, valley version.

Touching Delta conjecture, valley version.

Let $n$ be a positive integer and let $k$ satisfy $k\leq n$. Let $\mathcal{M P F}_{n,k}$ be the set of valley-marked parking functions of size $n$ with $k$ marked valleys and label…

Let $\Lambda$ be the ring of symmetric functions, let $\nabla$ and the Delta operators act on it, and let $\phi$ be defined by … For a composition…

Let $D$ be a partially labelled decorated Dyck path of size $n+m$ with $m$ zero labels, $n$ nonzero labels, and $k$ decorated rises. Its area word is $a(D)=a_1(D)\cdots a_{n+m}(D)$…

Garsia–Haiman conjecture. The function $C_n(q,t)$ is a polynomial in $q$ and $t$ with nonnegative coefficients, and there is a statistic $\mathrm{unknown}(w)$ on $n$-Dyck paths suc…

Let ${\mathcal PF}_n$ be the collection of parking functions in the $n\times n$ lattice square. For a parking function $PF$, let $p(PF)$ be its diagonal composition, and let…