Breadth

The most vertices at any one depth.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001058via OrderedTree✓↗

Breadth(tree)The most vertices at any one depth.

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.
• The largest number of nodes on one level, called breadth to keep width for posets.

Definition

Epsil, as the implementation runs it.

on OrderedTree, over _x

Apply(
       Function(0 if Length(level) == 0 else Max(
                                                  Length(level),
                                                  self(
                                                        self,
                                                        Fold(Function(
                                                                       Join(
                                                                             a,
                                                                             b,
                                                                           ),
                                                                       a,
                                                                       b,
                                                                     ), [], level),
                                                      ),
                                                ), self, level),
       Function(0 if Length(level) == 0 else Max(
                                                  Length(level),
                                                  self(
                                                        self,
                                                        Fold(Function(
                                                                       Join(
                                                                             a,
                                                                             b,
                                                                           ),
                                                                       a,
                                                                       b,
                                                                     ), [], level),
                                                      ),
                                                ), self, level),
       [_x],
     )

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [[]]

live ↗

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

Known value · FindStat St001058

FindStat's value for [[[]]]

live ↗

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

Known value · FindStat St001058

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

live ↗

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

Known value · FindStat St001058

About

Examples	4
Crosswalk	FindStat