On super Catalan polynomials

Abstract

We present a $q$-analog of the super Catalan number $(2m)!(2n)!/2m!n!(m+n)!$, which also generalizes the $q$-Catalan numbers $c_n(\lambda )$, due to Fürlinger and Hofbauer, for $\lambda =0$ and $\lambda =1$. We give a combinatorial interpretation for this analog when $m=2$.

10 pages, 4 figures

References in corpus (2)

• A q-rious positivity
• A Combinatorial Interpretation of The Numbers $6(2n)!/n!(n+2)!$

Cited by in corpus (2)

• A weighted interpretation for the super Catalan numbers
• Some observations about super Catalan numbers, corresponding orthogonal polynomials, and their q-analogues