- #1
Dragonfall
- 1,030
- 4
What is the expected number of fixed points in permutations? I got 1 as answer.
Fixed points in permutations refer to the elements in a permutation that remain in the same position after the permutation has been applied.
Fixed points can be calculated by comparing the original permutation with the resulting permutation after it has been applied. Any elements that are in the same position in both permutations are considered fixed points.
Fixed points in permutations are important because they provide information about the structure and properties of the permutation. They can also be used in various mathematical and scientific applications, such as in cryptography and group theory.
Yes, a permutation can have multiple fixed points. In fact, the maximum number of fixed points a permutation can have is equal to its length.
Fixed points and cycles are closely related in permutations. A fixed point can be seen as a cycle with a length of 1, while cycles of length greater than 1 do not have any fixed points. In other words, the number of fixed points in a permutation is equal to the number of cycles of length 1.