3 problems

Let $n$ and $r$ be positive integers, let $0\leqslant j\leqslant 2r-1$, and let $C_n(q)$ and $N_q(2n+1,n+k+1)$ denote the q-Catalan and q-Narayana quantities used in the paper. Pos…

Let $m$ be a positive integer, let $n_1,\ldots,n_m$ be positive integers, and set $n_{m+1}=n_1$. Let $j$ be an integer and let $r$ be a non-negative integer. The cyclic q-Narayana-…

Let $n$ and $r$ be positive integers, and let $a$ be a non-negative integer. Define the $q$-Narayana numbers by … Let $E_{n,r,a,j}(q)$ denote the Laurent polynomial expression in t…