InverseCyclicShift

Rotate the word one place to the right.

InverseCyclicShift(Permutation)Rotate the word one place to the right.

Typed signatures

Type	Package	Applies
`((binary_word) -> binary_word) & ((composition) -> composition) & ((parking_function) -> parking_function) & ((permutation) -> permutation) & ((set_composition) -> set_composition)`	`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.
Also takes a SetComposition, returning a SetComposition: The last block moved to the front.
FindStat's Mp00291.
Also takes a IntegerComposition, returning a IntegerComposition: Rotate the parts one place to the right: the last part moves to the front.
Also takes a BinaryWord, returning a BinaryWord: Rotate the word one place to the right: the last letter moves to the front.
Also takes a ParkingFunction, returning a ParkingFunction: Rotate the word one place to the right: the last entry moves to the front.

Examples

Basic #

the one-line word $231$

\mathrm{InverseCyclicShift}({\operatorname{Permutation}}([2, 3, 1]))

Out

{\operatorname{Permutation}}([1, 2, 3])

the set composition $\{2,4\} \mid \{1\} \mid \{3\}$

\mathrm{InverseCyclicShift}({\operatorname{SetComposition}}([[2, 4], [1], [3]]))

Out

{\operatorname{SetComposition}}([[3], [2, 4], [1]])

the composition $2 + 1 + 3$

\mathrm{InverseCyclicShift}({\operatorname{IntegerComposition}}([2, 1, 3]))

Out

{\operatorname{IntegerComposition}}([3, 2, 1])

the binary word $01100$

\mathrm{InverseCyclicShift}({\operatorname{BinaryWord}}([0, 1, 1, 0, 0]))

Out

{\operatorname{BinaryWord}}([0, 0, 1, 1, 0])

the parking function $2113$

\mathrm{InverseCyclicShift}({\operatorname{ParkingFunction}}([2, 1, 1, 3]))

Out

{\operatorname{ParkingFunction}}([3, 2, 1, 1])

About

Examples	5
Crosswalk	FindStat ×4