# Bijection between binary trees and plane trees?

I would like to describe a bijection between binary trees and plane trees. A binary tree has a root node and each node of the tree has at most 2 children (left and right). A plane tree has a root node and the children of each node are ordered from left to right. Can someone enlighten me on this? Thanks!

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There is a way of encoding n-ary trees into binary: the left is a son and the right is a brother. Are you looking along those lines, could you provide some context? – dtldarek Dec 4 '12 at 18:41
@dtldarek: Indeed. Left-child right-sibling binary tree, in wikipedia terminology. Can you make that an answer, so we can +1 it? – Hendrik Jan Dec 4 '12 at 21:37

There is a way of encoding n-ary trees into binary: the left is a son and the right is a brother; here is the Wikipedia's entry.

I think the following algorithm will work: Lets suppose the Root node of a plain tree has n children, then we count $min (k): 2^k <= n$ Next we build the 3-level binary tree with Root node = Root node of the plain tree and intermediate nodes also = Root node of the plain tree.