On super Catalan polynomials

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

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