The collection of these transformations forms the symmetric group.
The collection of these transformations forms the symmetric group. The parity of one of these is given by the nonzero values of the Levi-Civita symbol. They are classified as odd or even depending on the number of transpositions they can be decomposed into. This is the name given to a bijection of a set onto itself, and those that reverse the order of a pair are known as inversions. A special type of these that leaves no object in its (*) original place is called a derangement. For n objects, the number of these is equal to n factorial, and unlike combinations they take the order of elements into account. Shuffling generates a random one. For 10 points, identify these arrangements of a set of objects in a particular order.
The collection of these transformations forms the symmetric group.
permutation [prompt on "bijection" or "isomorphism"]