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In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation. A circular shift is a special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a circular shift is a permutation σ of the n entries in the tuple such that either

or

The result of repeatedly applying circular shifts to a given tuple are also called the circular shifts of the tuple.

For example, repeatedly applying circular shifts to the four-tuple successively gives

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