PositiveCycleType

The lengths of the positive cycles, largest first: those of the underlying permutation with an even number of negative entries.

FindStatMp00166via SignedPermutation↗

PositiveCycleType(SignedPermutation)The lengths of the cycles with an even number of negative entries, largest first.

Typed signatures

Type	Package	Applies
(signed_permutation) -> integer_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a SignedPermutation and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00166, "even cycle type". Geck and Pfeiffer's positive cycles.

Examples

Basic #

the signed permutation $2\,\bar 3\,1$

live ↗

In$\mathrm{PositiveCycleType}({\operatorname{SignedPermutation}}([2, -3, 1]))$Out${\operatorname{IntegerPartition}}([])$

About

Examples	1
Crosswalk	FindStat