Séminaire Lotharingien de Combinatoire, B53e (2006), 16 pp.
Some Bijections and Identities for the Catalan and Fine Numbers
We establish combinatorial interpretations
of several identities for the Catalan
and Fine numbers. Analytic proofs are outlined and we also give
combinatorial proofs utilizing some new bijections of independent interest.
counts ordered trees on n edges by number of interior vertices adjacent to a
counts Dyck n-paths by number of long interior
inclines. We also give an analogue for the Fine numbers of Touchard's
Catalan number identity.
Received: February 17, 2005.
Accepted: January 4, 2006.
Final Version: February 22, 2006.
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