A Weighted Interpretation for the Super Catalan Numbers
Emily Allen and Irina Gheorghiciuc
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
The super Catalan numbers T(m,n)=(2m)!(2n)!/2m!n!(m+n)! are integers that generalize the Catalan numbers. With the exception of a few values of m, no combinatorial interpretation is 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.
Full version: pdf,
(Concerned with sequences
August 26 2014; revised version received August 31 2014; September 11 2014.
Published in Journal of Integer Sequences, November 5 2014.
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