Lattice Points and Rational $q$-Catalan Numbers

Drew Armstrong

For each pair of coprime integers $a$ and $b$ we have a rational $q$-Catalan number $\mathrm{Cat}(a,b{)}_q={\left(\genfrac{}{}{0ex}{}{a+b}{a}\right)}_q/[a+b{]}_q$. It is known that this is a polynomial in $…