what is cycil permutation?

Qawsw

5 months ago

Cyclic permutation is a way of rearranging objects in a circle where the order matters, but rotations of the same arrangement are considered the same.

Simple explanation:

Imagine you have 3 letters: A, B, C.

If you arrange them in a line, ABC, ACB, BAC, etc., each is different.

But if you arrange them in a circle, then ABC, BCA, and CAB are considered the same cyclic permutation because you can rotate the circle to get the others.


Key point:
Cyclic permutations count arrangements around a circle, ignoring rotations.

Formula:

Number of cyclic permutations of n objects = (n − 1)!


Example:

4 friends sitting around a table → number of arrangements = (4−1)! = 3! = 6


In short, cyclic permutation is circular arrangement where rotation doesn’t create a new arrangement.