HookLengthOfFirstCell

The hook length of cell (1,1): the largest part plus the number of parts, less one.

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HookLengthOfFirstCell(partition)The hook length of cell (1,1): the largest part plus the number of parts, less one.

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.

Examples

Basic #

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

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

Out

6

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

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

Out

5

Properties #

FindStat's value for [1]

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

Out

1

Known value · FindStat St000459

FindStat's value for [2]

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

Out

2

Known value · FindStat St000459

FindStat's value for [3]

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

Out

3

Known value · FindStat St000459

About

Examples	5
Crosswalk	FindStat