Bijections for ternary trees and non-crossing trees

@article{Panholzer2002BijectionsFT,
  title={Bijections for ternary trees and non-crossing trees},
  author={Alois Panholzer and Helmut Prodinger},
  journal={Discrete Mathematics},
  year={2002},
  volume={250},
  pages={181-195}
}
The number Nn of non-crossing trees of size n satis/es Nn+1 = Tn where Tn enumerates ternary trees of size n. We construct a new bijection to establish that fact. Since Tn=(1=(2n+ 1))( 3n n ), it follows that 3(3n− 1)(3n− 2)Tn−1 = 2n(2n+ 1)Tn. We construct two bijections “explaining” this recursion; one of them easily extends to the case of t-ary trees. c © 2002 Elsevier Science B.V. All rights reserved. 
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