Combinatorial Proofs Of Some Q-Series Identities Related To The Catalan Recurrence Relation

We know that the Catalan numbers satisfy the following recurrence relationwhere C_k:=(?)((?)) is called the k-th Catalan number. It is easy to see that (*) has a q-analogue as follows:By applying the model of partitions of integers and a related theorem due to Chapman, using conjugations of the Young diagram, and establishing weigh-preservingand sign-reversing involutions, we give combinatorial interpretations of (**) and the following two identities:...