HalfPerimeter

Half the perimeter of the bounding rectangle of the Young diagram: largest part plus number of parts.

HalfPerimeter(partition)Half the perimeter of the bounding rectangle of the Young diagram: largest part plus number of parts.

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.
FindStat's St000459 calls the hook length of the base cell the perimeter; that is HookLengthOfFirstCell, one less than this.

Definition

Epsil, as the implementation runs it.

on IntegerPartition, over _x

0 if Length(_x) < 1 else Max(_x) + Length(_x)

Basic #

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

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

Out

7

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

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

Out

6

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Examples	2