5 problems

For coprime positive integers $a,b$, let $C_{b,-a,a,b}(q,t)$ be the generalized q,t-Catalan polynomial defined using the sweep map, and let $[j]_q$ denote the q-integer and…

Let $a$ and $b$ be relatively prime positive integers. Let $\mathfrak{D}_{a,b}$ be the set of $(a,b)$-Dyck paths, and let … be the image of the pair $(\zeta,\eta)$. Uniqueness conj…

For $a,b\geq 0$, define the q,t-rectangle numbers … Here $\mathsf{area}^*_{b,-a}$ is the adjusted area statistic defined using the minimum of the $(b,-a)$-levels. Joint symmetry co…

Joint symmetry conjecture. For all $r,s\in\mathbb{Z}$ and all $a,b\geq 0$,

Let $A=x_1,\ldots,x_k\}$ be an alphabet and $\operatorname{wt}:A\rightarrow\mathbb{Z}$ a weight function. For nonnegative integers $n_1,\ldots,n_k$, let…