3 problems

Let $m$ and $k$ be nonnegative integers, let $p$ and $q$ be parameters, and let $Z_p$ be the generator appearing in the $(p,q)$-deformed generalized Weyl algebra. Write $[i]_{p,q}$…

Let $A_{n+1}$ be the matrix whose characteristic equation is denoted by $Q_{n+1}(x)$, and let $(x-1)^{n+1}_{F}$ denote the Golden Binomial. Characteristic-polynomial conjecture. Th…

q-Rodrigues conjecture. The identity