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A New Combinatorial Identity for Catalan Numbers

Aker, Kursat
Gursoy, Aysin Erkan
In this article, we prove a conjecture about the equality of two generating functions described in "From Parking Functions to Gelfand Pairs (Aker, Can 2012)" attached to two sets whose cardinalities are given by Catalan numbers: We establish a combinatorial bijection between the two sets on which the two generating functions were based on.