7 problems

Let … . Negut positivity conjecture. The coefficients in the Negut formula are positive whenever the partition lies under a certain convex curve. This is presented as Conjecture 7.…

Let $m,n>0$, let $\mathcal{P}_{m,n}$ be the set of $(m,n)$-parking functions, let $\sigma(\pi)$ be the word of $\pi$, let $\mu\models n$ be a composition, and let $\mathbb{S}$ be t…

Let $\mathcal{P}_{3,n}$ be the set of $(3,n)$-parking functions, let $\operatorname{pides}(\pi)=2^a1^b$, let $\Phi$ be the involution whose fixed points are the fixed parking funct…

The constant term formula under discussion defines an additional parameter $t$ for the $(m,n)$-Schröder parking-function enumerator. $(q,t)$-enumeration conjecture. It corresponds…

Armstrong's rank and co-skew-length symmetry conjecture. The following $q,t$-polynomials are equal:

Let $\mathsf{PF}_{a,b}(q,t)$ be the symmetric function defined from rational parking functions, and let ${\sf Sch}_{a,b;k}(q,t)$ denote the coefficient of $s_{(k+1,1^{a-k-1})}$ in…

Let $\mathsf{PF}_n$ be the set of labeled classical parking functions. For $P\in\mathsf{PF}_n$, let $\mathsf{area}(P)$ be its area statistic and let $\mathsf{dinv}(P)$ be its diago…