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CyclicShift from Permutation ​

Rotate the word one place to the left.

Permutation → Permutationinverse

Called as CombinatorialMap(x, "CyclicShift"). The head's page has its examples.

Live

FindStat Mp00279

Backward Rotation

Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

BijectionGraded mapas FindStat records them, checked by FindStat's contributors.

Rotates a permutation by moving the first entry last.
ObjectImage
[1][1]
[1,2][2,1]
[2,1][1,2]
[1,2,3][2,3,1]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00279 has the rest.