On uniformly regular measures
On binary trees and Dyck paths
A bijection between the set of binary trees with n vertices and the set of Dyck paths of length 2n is obtained. Two constructions are given which enable to pass from a Dyck path to a binary tree and from a binary tree to a Dyck path.
On binary trees and permutations
Every binary tree is associated to a permutation with repetitions, which determines it uniquely. Two operations are introduced and used for the construction of the set of all binary trees. The set of all permutations which correspond to a given binary tree is determined and its cardinal number is evaluated.
Counting peaks and valleys in -colored Motzkin paths.
On -colored Motzkin words.
On the dominance partial ordering of Dyck paths.
Recursive generation of -ary trees.
General results on the enumeration of strings in Dyck paths.
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