12 problems

Euler-number specialization conjecture.

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

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.

Generalised Delta square conjecture, valley version.

Generalised Delta square conjecture, rise version.

Generalised 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 $a(D)=a_1(D)\cdots a_{n+m}(D)$…