InvariantSubsetCount

Subsets of the points left invariant by a permutation with these cycle lengths: each cycle is in or out, 2 to the number of cycles.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000511via IntegerPartition✓↗

InvariantSubsetCount(partition)Subsets of the points left invariant by a permutation with these cycle lengths: each cycle is in or out, 2 to the number of cycles.

Typed signatures

Type	Package	Applies
(integer_partition) -> number	combinatorics	always

Domain: Partition statistics

Details

• Defined over IntegerPartition as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a IntegerPartition 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 IntegerPartition, over _x

1 if Length(_x) < 1 else 2 ^ Length(_x)

Examples

Basic #

the partition $4 + 2 + 1$ of $7$

live ↗

In$\mathrm{InvariantSubsetCount}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$8$

the partition $3 + 3 + 1$ of $7$

live ↗

In$\mathrm{InvariantSubsetCount}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$8$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([1]), \text{InvariantSubsetCount})$Out$2$

Known value · FindStat St000511

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([2]), \text{InvariantSubsetCount})$Out$2$

Known value · FindStat St000511

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{InvariantSubsetCount})$Out$2$

Known value · FindStat St000511

About

Examples	5
Crosswalk	FindStat