Some bijections and identities for the Catalan and Fine numbers.

@inproceedings{Callan2005SomeBA,
  title={Some bijections and identities for the Catalan and Fine numbers.},
  author={David Callan},
  year={2005}
}
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. We show that Cn = 1 n+1 ∑ k ( n+1 2k+1 )( n+k k ) counts ordered trees on n edges by number of interior vertices adjacent to a leaf and Cn = 2 n+1 ∑ k ( n+1 k+2 )( n−2 k ) counts Dyck n-paths by number of long interior inclines. We also give an analogue for the Fine numbers of… CONTINUE READING

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