Abstract
The number N n of non-crossing trees of size n satisfies N n+1=T n where T n enumerates ternary trees of size n. We construct a new bijection to establish that fact. Since T n=(1/(2n+1))( 3n n ) , it follows that 3(3n−1)(3n−2)T n−1=2n(2n+1)T n . We construct two bijections “explaining” this recursion; one of them easily extends to the case of t-ary trees.
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