CollessIndex

The sum, over the nodes, of how much the node counts of the two subtrees differ.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001376via BinaryTree✓↗

CollessIndex(tree)The sum, over the nodes, of how much the node counts of the two subtrees differ.

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.

Definition

Epsil, as the implementation runs it.

on BinaryTree, over _x

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

Examples

Basic #

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

live ↗

In$\mathrm{CollessIndex}({\operatorname{BinaryTree}}(\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, \bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, 0\bigr\rbrack\bigr\rbrack))$Out$2$

Properties #

FindStat's value for [.,.]

live ↗

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

Known value · FindStat St001376

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

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryTree}}(\bigl\lbrack0, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack), \text{CollessIndex})$Out$1$

Known value · FindStat St001376

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

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryTree}}(\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, 0\bigr\rbrack), \text{CollessIndex})$Out$1$

Known value · FindStat St001376

About

Examples	4
Crosswalk	FindStat