Bijections for ternary trees and non-crossing trees Original Research Article

The number Nn of non-crossing trees of size n satisfies 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))(3nn), 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.