LongestPathVertexCount

The most vertices on a path from the root: the height plus one.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000094via OrderedTree✓↗

LongestPathVertexCount(tree)The most vertices on a path from the root: the height plus one.

Typed signatures

Type	Package	Applies
(ordered_tree) -> number	combinatorics	always

Domain: Tree statistics

Details

• 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.
• FindStat calls this the depth of an ordered tree.

Definition

Epsil, as the implementation runs it.

on OrderedTree, over _x

Apply(
       Function(1 if Length(t) == 0 else 1 + Fold(
                                                   Function(Max(a, b), a, b),
                                                   0,
                                                   Map(Function(
                                                                 self(self, c),
                                                                 c,
                                                               ), t),
                                                 ), self, t),
       Function(1 if Length(t) == 0 else 1 + Fold(
                                                   Function(Max(a, b), a, b),
                                                   0,
                                                   Map(Function(
                                                                 self(self, c),
                                                                 c,
                                                               ), t),
                                                 ), self, t),
       _x,
     )

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [[]]

live ↗

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

Known value · FindStat St000094

FindStat's value for [[[]]]

live ↗

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

Known value · FindStat St000094

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

live ↗

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

Known value · FindStat St000094

About

Examples	4
Crosswalk	FindStat