These three and the identity permutation leave the cross ratio unaltered.
2.
The parity of an Identity Permutation is always even.
3.
At the end we get the identity permutation, whose " N " ( see above ) is zero.
4.
The orbit of a 1-cycle is called a " fixed point " of the permutation, but as a permutation every 1-cycle is the identity permutation.
5.
It is the number of crossings in the arrow diagram of the permutation, its Kendall tau distance from the identity permutation, and the sum of each of the inversion related vectors defined below.
6.
The identity permutation, which consists only of 1-cycles, can be denoted by a single 1-cycle ( x ), by the number 1, or by " id ".
7.
A transitive permutation group is " regular " ( or sometimes referred to as " sharply transitive " ) if the only permutation in the group that has fixed points is the identity permutation.
8.
Z 3 = { 0, 1, 2 } with addition modulo 3; group element 0 corresponds to the identity permutation e, group element 1 to permutation ( 123 ), and group element 2 to permutation ( 132 ).
9.
To bring a permutation with " k " inversions into order ( i . e ., transform it into the identity permutation ), by successively applying ( right-multiplication by ) adjacent transpositions, is always possible and requires a sequence of " k " such operations.
10.
In the case of automata with binary-valued states ( zero or one ), there are only two possible permutations on the states ( the identity permutation and the permutation that swaps the two states ), which may themselves be represented as the exclusive or of a state with a binary value.
मोबाइल