A weighted interpretation for the super Catalan numbers

Abstract

The super Catalan numbers $T(m,n)=(2m)!(2n)!/2m!n!(m+n)!$ are integers which generalize the Catalan numbers. With the exception of a few values of $m$, no combinatorial interpretation in known for $T(m,n)$. We give a weighted interpretation for $T(m,n)$ and develop a technique that converts this weighted interpretation into a conventional combinatorial interpretation in the case $m=2$.

8 pages, 5 figures

References in corpus (2)

• A Combinatorial Interpretation of The Numbers $6(2n)!/n!(n+2)!$
• On super Catalan polynomials

Cited by in corpus (1)

• Chase-escape with death on trees