Leaves

The number of leaves, the vertices with no children.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000201via BinaryTree✓↗St000167via OrderedTree✓↗

Leaves(tree)The number of leaves, the vertices with no children.

Typed signatures

Type	Package	Applies
(binary_tree | labeled_tree | ordered_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.
• Defined over OrderedTree as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a OrderedTree 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 (1 if t[1] in Integers && t[2] in
                                                                  Integers else 0) +
                                        self(self, t[1]) + self(self, t[2]), self, t),
       Function(0 if t in Integers else (1 if t[1] in Integers && t[2] in
                                                                  Integers else 0) +
                                        self(self, t[1]) + self(self, t[2]), self, t),
       _x,
     )

on OrderedTree, over _x

Apply(Function(
                1 if Length(t) == 0 else Sum(Map(Function(self(self, c), c), t)),
                self,
                t,
              ), Function(1 if Length(t) == 0 else Sum(Map(
                                                           Function(self(
                                                                          self,
                                                                          c,
                                                                        ), c),
                                                           t,
                                                         )), self, t), _x)

Examples

Basic #

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

live ↗

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

the ordered tree $[[],[[]],[]]$

live ↗

In$\mathrm{Leaves}({\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack\bigr\rbrack))$Out$3$

the labeled tree with edges $12, 23, 24$

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{LabeledTree}}([[1, 2], [2, 3], [2, 4]]), \text{Leaves})$Out$3$

Properties #

FindStat's value for [.,.]

live ↗

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

Known value · FindStat St000201

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

live ↗

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

Known value · FindStat St000201

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

live ↗

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

Known value · FindStat St000201

FindStat's value for [[]]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack), \text{Leaves})$Out$1$

Known value · FindStat St000167

FindStat's value for [[[]]]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack), \text{Leaves})$Out$1$

Known value · FindStat St000167

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

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack\bigr\rbrack), \text{Leaves})$Out$2$

Known value · FindStat St000167

About

Examples	9
Crosswalk	FindStat ×2