ConjugateAfterCycleType

The conjugate partition of the cycle type.

ConjugateAfterCycleType(Permutation)The conjugate partition of the cycle type.

Typed signatures

Type	Package	Applies
(permutation) -> integer_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Entry j is the count of cycles of length at least j — non-increasing in j by construction, so it comes out sorted without needing one.

Examples

Basic #

the one-line word $231$

live ↗

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

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Examples	1