RightBranchOrderedTree

A binary tree as an ordered tree with one more vertex: a right child becomes its parent's right brother, a left child its parent's first child.

FindStatMp00015via BinaryTree↗

RightBranchOrderedTree(BinaryTree)A binary tree as an ordered tree with one more vertex: a right child becomes its parent's right brother, a left child its parent's first child.

Typed signatures

Type	Package	Applies
(binary_tree) -> ordered_tree	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a BinaryTree and returns a OrderedTree — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00015, Sage's to_ordered_tree_right_branch, a bijection. Its inverse is RightBranchBinaryTree. OrderedTree(BinaryTree) is the left-branch bijection, which is the constructor.

Examples

Basic #

a four-node tree

live ↗

In$\mathrm{RightBranchOrderedTree}({\operatorname{BinaryTree}}(\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, \bigl\lbrack0, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack\bigr\rbrack))$Out${\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack\bigr\rbrack)$

About

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