ContentSum

The sum of the contents j - i of the cells.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000509via IntegerPartition✓↗

ContentSum(partition)The sum of the contents j - i of the cells.

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

0 if Length(_x) < 1 else Sum(Map(Function(
                                           _x[i] * (_x[i] + 1) / 2 - i * _x[i],
                                           i,
                                         ), Range(1, Length(_x))))

Examples

Basic #

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

live ↗

In$\mathrm{ContentSum}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$3$

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

live ↗

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

Properties #

FindStat's value for [2]

live ↗

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

Known value · FindStat St000509

FindStat's value for [3]

live ↗

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

Known value · FindStat St000509

FindStat's value for [4]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([4]), \text{ContentSum})$Out$6$

Known value · FindStat St000509

About

Examples	5
Crosswalk	FindStat