LongCycleConjugation

Conjugation by the long cycle (1 2 ... n): each cycle's entries shifted up by one, cyclically.

FindStatMp00265via Permutation↗

LongCycleConjugation(Permutation)Conjugation by the long cycle (1 2 ... n): each cycle's entries shifted up by one, cyclically.

Typed signatures

Type	Package	Applies
(permutation) -> permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Reflects the permutation's cycle diagram around the circle one step; it fixes the cycle type, and its n-th power is the identity.

Examples

Basic #

the one-line word $231$

live ↗

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

About

Examples	1
Crosswalk	FindStat