PermutationOrder Property

public long Order { get; }

Public ReadOnly Property Order As Long
	Get

public:
property long long Order {
	long long get ();
}

member Order : int64 with get

Property Value

The order of a permutation is the number of times it must be applied in order to return all elements to their original position. Stated differently, the order of a permutation is the smallest power to which it must be raised to obtain the identity permutation.

Some permutations with dimension greater than about 300 have an order larger than MaxValue; for these permutations the returned value will overflow.

Note that the word order is also used to refer to the number of distinct permutations of a given dimension. That "order" is a property of the permutation group. This "order" is a property of each permutation.

In no circumstances does "order" refer to the number of elements on which a permutation operates; that is the Dimension of the permutation.

Reference