MaximalLeftBranches

The number of maximal paths of left edges.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000919via BinaryTree✓↗

MaximalLeftBranches(tree)The number of maximal paths of left edges.

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.
• A branch starts at a node with a left child that is not itself a left child.

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

Examples

Basic #

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

live ↗

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

Properties #

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

live ↗

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

Known value · FindStat St000919

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

live ↗

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

Known value · FindStat St000919

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

live ↗

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

Known value · FindStat St000919

About

Examples	4
Crosswalk	FindStat