Circular Permutation Table ((n−1)!)
Enter a maximum number of items n to list the count of circular permutations (n−1)! for n = 1 up to that value. Counts arrangements around a circle where rotations are treated as identical, computed exactly with BigInt.
Input
Enter the maximum number of items n to arrange around a circle, and see a table of the circular permutation count (n−1)! from n = 1 up to that value.
Enter a whole number from 1 to 30.
Result
Circular permutations for n = 8
5,040
Circular permutation table
Each row shows the number of items n and its circular permutation count (n−1)!.
| Items n | Circular permutations (n−1)! |
|---|---|
| 1 | 1 |
| 2 | 1 |
| 3 | 2 |
| 4 | 6 |
| 5 | 24 |
| 6 | 120 |
| 7 | 720 |
| 8 | 5,040 |
Circular permutation formula
(n−1)!
A circular permutation counts arrangements of n distinct items around a circle. Because rotations that match are treated as the same, the total is (n−1)!.
How it works
- A circular permutation counts the ways to arrange n distinct items around a circle, where arrangements that match after rotation are treated as the same.
- The number of circular permutations equals (n−1)!. This is the linear count n! divided by the n equivalent rotations.
- For n = 1 the value is 1, for n = 2 it is 1, and for n = 3 it is 2.
- This table lists (n−1)! from n = 1 up to the maximum value you enter.
- If arrangements that match after flipping are also treated as the same, you get a necklace permutation, which uses a different formula.
- BigInt is used so large values are computed exactly without overflow.
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Circular Permutation Table ((n−1)!)