TamariBinaryTree

A path D = L U R D as the binary tree whose left and right subtrees are those of L and R: the bijection compatible with the Tamari order.

FindStatMp00029via DyckPath↗

TamariBinaryTree(DyckPath)A path D = L U R D as the binary tree whose left and right subtrees are those of L and R: the bijection compatible with the Tamari order.

Typed signatures

Type	Package	Applies
(dyck_path) -> binary_tree	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a BinaryTree — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Defined as a COMPOSITION, applied right to left: Mirror after BinaryTree after ReverseComplement. Each step goes through its own declared head, so every intermediate value is a properly constructed carrier.
• FindStat's Mp00029; TamariDyckPath is its inverse. BinaryTree(DyckPath) reads the other decomposition, U L D R, so this is it after a reverse-complement and a left-right mirror.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{TamariBinaryTree}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{BinaryTree}}(\bigl\lbrack\bigl\lbrack0, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack, 0\bigr\rbrack)$

About

Examples	1
Crosswalk	FindStat

See also: Mirror, BinaryTree, ReverseComplement