LargestOutDegree

The most children any vertex has.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000328via OrderedTree✓↗

LargestOutDegree(tree)The most children any vertex has.

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.

Definition

Epsil, as the implementation runs it.

on OrderedTree, over _x

Apply(
       Function(
                 0 if Length(t) == 0 else Max(
                                               Length(t),
                                               Fold(
                                                     Function(Max(a, b), a, b),
                                                     0,
                                                     Map(
                                                          Function(
                                                                    self(
                                                                          self,
                                                                          c,
                                                                        ),
                                                                    c,
                                                                  ),
                                                          t,
                                                        ),
                                                   ),
                                             ),
                 self,
                 t,
               ),
       Function(
                 0 if Length(t) == 0 else Max(
                                               Length(t),
                                               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$\mathrm{LargestOutDegree}({\operatorname{OrderedTree}}(\bigl\lbrack\bigl\lbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigr\rbrack\bigr\rbrack))$Out$3$

Properties #

FindStat's value for [[]]

live ↗

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

Known value · FindStat St000328

FindStat's value for [[[]]]

live ↗

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

Known value · FindStat St000328

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

live ↗

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

Known value · FindStat St000328

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Examples	4
Crosswalk	FindStat