SeaweedAlgebraDimension

The dimension of the maximal parabolic seaweed algebra: half the sum of the squares of the parts and of the size.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001262via IntegerPartition✓

SeaweedAlgebraDimension(partition)The dimension of the maximal parabolic seaweed algebra: half the sum of the squares of the parts and of the size.

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] ^ 2, i), Range(1, Length(_x)))) +
                          Sum(_x) ^ 2) / 2

Basic #

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

\mathrm{SeaweedAlgebraDimension}({\operatorname{IntegerPartition}}([4, 2, 1]))

Out

35

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

\mathrm{SeaweedAlgebraDimension}({\operatorname{IntegerPartition}}([3, 3, 1]))

Out

34

Properties #

FindStat's value for [1]

\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([1]), \text{SeaweedAlgebraDimension})

Out

1

Known value · FindStat St001262

FindStat's value for [2]

\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([2]), \text{SeaweedAlgebraDimension})

Out

4

Known value · FindStat St001262

FindStat's value for [3]

\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{SeaweedAlgebraDimension})

Out

9

Known value · FindStat St001262

About

Examples	5
Crosswalk	FindStat