ForkRightRightLeftPatternCount

The number of nodes with two children whose right child's right child has a left child.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000132via BinaryTree✓↗

ForkRightRightLeftPatternCount(tree)The number of nodes with two children whose right child's right child has a left child.

Typed signatures

Type	Package	Applies
(binary_tree) -> number	combinatorics	always

Domain: Tree statistics

Details

• Defined over BinaryTree as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a BinaryTree and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• FindStat's St000132: the contiguous pattern [[.,.],[.,[[.,.],.]]], whose empty slots match any subtree.

Definition

Epsil, as the implementation runs it.

on BinaryTree, over _x

Apply(
       Function(0 if t in Integers else (0 if t[1] in Integers else 0 if t[2] in
                                                                         Integers else 0 if t[2][2] in Integers else 0 if t[2][2][1] in Integers else 1) +
                                        self(self, t[1]) + self(self, t[2]), self, t),
       Function(0 if t in Integers else (0 if t[1] in Integers else 0 if t[2] in
                                                                         Integers else 0 if t[2][2] in Integers else 0 if t[2][2][1] in Integers else 1) +
                                        self(self, t[1]) + self(self, t[2]), self, t),
       _x,
     )

Examples

Basic #

the binary tree $[[.,.],[[.,.],.]]$

live ↗

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

Properties #

FindStat's value for [.,.]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryTree}}(\bigl\lbrack0, 0\bigr\rbrack), \text{ForkRightRightLeftPatternCount})$Out$0$

Known value · FindStat St000132

FindStat's value for [.,[.,.]]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryTree}}(\bigl\lbrack0, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack), \text{ForkRightRightLeftPatternCount})$Out$0$

Known value · FindStat St000132

FindStat's value for [[.,.],.]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryTree}}(\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, 0\bigr\rbrack), \text{ForkRightRightLeftPatternCount})$Out$0$

Known value · FindStat St000132

About

Examples	4
Crosswalk	FindStat