DeBruijnMorselt

The right-branch bijection to binary trees followed by the left-branch bijection back: the de Bruijn-Morselt automorphism of the ordered trees.

FindStatMp00328via OrderedTree↗

DeBruijnMorselt(OrderedTree)The right-branch bijection to binary trees followed by the left-branch bijection back: the de Bruijn-Morselt automorphism of the ordered trees.

Typed signatures

Type	Package	Applies
(ordered_tree) -> ordered_tree	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a OrderedTree and returns a OrderedTree — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Defined as a COMPOSITION, applied right to left: OrderedTree after RightBranchBinaryTree. Each step goes through its own declared head, so every intermediate value is a properly constructed carrier.
• FindStat's Mp00328. Chaotic in general: Shapiro shows its sixth power is the identity on the trees that correspond to compositions.

Examples

Basic #

an ordered tree with four edges

live ↗

In$\mathrm{DeBruijnMorselt}({\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack\bigr\rbrack))$Out${\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack)$

About

Examples	1
Crosswalk	FindStat

See also: OrderedTree, RightBranchBinaryTree