SwapEquivalentTreeCountLog

The binary logarithm of the number of binary trees with the same underlying rooted tree: the nodes whose two subtrees differ up to swaps.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000414via BinaryTree✓↗

SwapEquivalentTreeCountLog(tree)The binary logarithm of the number of binary trees with the same underlying rooted tree: the nodes whose two subtrees differ up to swaps.

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.
• FindStat's St000414.

Definition

Epsil, as the implementation runs it.

on BinaryTree, over _x

Apply(
       Function(0 if t in Integers else (0 if Apply(
                                                     Function(
                                                               (True if b in
                                                                        Integers else False) if a in Integers else False if b in Integers else (True if self(self, a[2], b[2]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False) if self(self, a[1], b[1]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False,
                                                               self,
                                                               a,
                                                               b,
                                                             ),
                                                     Function(
                                                               (True if b in
                                                                        Integers else False) if a in Integers else False if b in Integers else (True if self(self, a[2], b[2]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False) if self(self, a[1], b[1]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False,
                                                               self,
                                                               a,
                                                               b,
                                                             ),
                                                     t[1],
                                                     t[2],
                                                   ) else 1) +
                                        self(self, t[1]) + self(self, t[2]), self, t),
       Function(0 if t in Integers else (0 if Apply(
                                                     Function(
                                                               (True if b in
                                                                        Integers else False) if a in Integers else False if b in Integers else (True if self(self, a[2], b[2]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False) if self(self, a[1], b[1]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False,
                                                               self,
                                                               a,
                                                               b,
                                                             ),
                                                     Function(
                                                               (True if b in
                                                                        Integers else False) if a in Integers else False if b in Integers else (True if self(self, a[2], b[2]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False) if self(self, a[1], b[1]) else self(self, a[2], b[1]) if self(self, a[1], b[2]) else False,
                                                               self,
                                                               a,
                                                               b,
                                                             ),
                                                     t[1],
                                                     t[2],
                                                   ) else 1) +
                                        self(self, t[1]) + self(self, t[2]), self, t),
       _x,
     )

Examples

Basic #

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

live ↗

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

Properties #

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

live ↗

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

Known value · FindStat St000414

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

live ↗

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

Known value · FindStat St000414

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

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryTree}}(\bigl\lbrack0, \bigl\lbrack0, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack\bigr\rbrack), \text{SwapEquivalentTreeCountLog})$Out$2$

Known value · FindStat St000414

About

Examples	4
Crosswalk	FindStat