CyclicShift

Rotate the word one place to the left.

CyclicShift(Permutation)Rotate the word one place to the left.

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 first block moved to the end.
FindStat's Mp00292.
Also takes a IntegerComposition, returning a IntegerComposition: Rotate the parts one place to the left: the first part moves to the end.
Also takes a BinaryWord, returning a BinaryWord: Rotate the word one place to the left: the first letter moves to the end.
Also takes a ParkingFunction, returning a ParkingFunction: Rotate the word one place to the left: the first entry moves to the end.

Examples

Basic #

the one-line word $231$

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

Out

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

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

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

Out

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

the composition $2 + 1 + 3$

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

Out

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

the binary word $01100$

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

Out

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

the parking function $2113$

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

Out

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

About

Examples	5
Crosswalk	FindStat ×5