DysonRank

Largest part minus number of parts.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaRank of a partitionWikidataQ7293214FindStatSt000145via IntegerPartition✓

DysonRank(partition)Largest part minus 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.

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

Out

1

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

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

Out

0

Properties #

FindStat's value for [1]

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

Out

0

Known value · FindStat St000145

FindStat's value for [2]

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

Out

1

Known value · FindStat St000145

FindStat's value for [3]

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

Out

2

Known value · FindStat St000145

About

Examples	5
Crosswalk	Wikipedia Wikidata FindStat