PowerSumSymmetricFunctionAtOne

The power-sum symmetric function indexed by the partition, in as many variables as it has parts, all set to 1: the number of parts to its own power.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001563via IntegerPartition✓↗

PowerSumSymmetricFunctionAtOne(partition)The power-sum symmetric function indexed by the partition, in as many variables as it has parts, all set to 1: the number of parts to its own power.

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 Length(_x) ^ Length(_x)

Examples

Basic #

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

live ↗

In$\mathrm{PowerSumSymmetricFunctionAtOne}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$27$

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

live ↗

In$\mathrm{PowerSumSymmetricFunctionAtOne}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$27$

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001563

FindStat's value for [2]

live ↗

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

Known value · FindStat St001563

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{PowerSumSymmetricFunctionAtOne})$Out$1$

Known value · FindStat St001563

About

Examples	5
Crosswalk	FindStat