A simple bijection between a subclass of 2-binary trees and ternary trees

). In this note we provide another bijection, which is simpler. Furthermore, it preserves more of the structure of the tree. The basic idea is that, when • ◦ is forbidden, any sequence of nodes connected by right edges must have labels white . . . white, followed by black . . . black. We translate the restricted 2-binary tree recursively into a ternary tree from the root to the leaves, by leaving right edges intact, and connecting the translated right subtree to the root as the right(most) subtree. Now, we look locally at the root, its left subtree and the longest chain of right edges, viz.