TamariDyckPath

The Dyck path T(L) U T(R) D of a tree with subtrees L and R: the bijection compatible with the Tamari order.

TamariDyckPath(BinaryTree)The Dyck path T(L) U T(R) D of a tree with subtrees L and R: the bijection compatible with the Tamari order.

Typed signatures

Type	Package	Applies
`(binary_tree) -> dyck_path`	`combinatorics`	always

Domain: Combinatorial maps

Details

Takes a BinaryTree and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
Defined as a COMPOSITION, applied right to left: ReverseComplement after DyckPath after Mirror. Each step goes through its own declared head, so every intermediate value is a properly constructed carrier.
FindStat's Mp00020; the inverse is TamariBinaryTree. DyckPath(BinaryTree) reads the other decomposition, U T(L) D T(R), so this is it after a left-right mirror and a reverse-complement.

Examples

Basic #

a four-node tree

\mathrm{TamariDyckPath}({\operatorname{BinaryTree}}(\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, \bigl\lbrack0, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack\bigr\rbrack))

Out

{\operatorname{DyckPath}}([1, 0, 1, 1, 1, 0, 0, 0])

About

Examples	1
Crosswalk	FindStat