The number of permutations of a set with elements is (see the rule of product).
In fact, every bijection of a set into itself gives a permutation, and any permutation gives rise to a bijective function.
Therefore, we can say that there are bijective functions from a set with elements into itself.
Moreover, if are two factorization of a permutation into transpositions, then and must be both even or both odd. So we can label permutations as even or odd depending on the number of transpositions for any decomposition.
Permutations (as functions) form in general a non-abelian group with function composition as binary operation called symmetric group of order . The subset of even permutations becomes a subgroup called the alternating group of order .
|Date of creation||2013-03-22 11:51:45|
|Last modified on||2013-03-22 11:51:45|
|Last modified by||alozano (2414)|