Given a finite set , a transposition is a permutation (bijective function of onto itself) such that there exist indices such that , and for all other indices . This is often denoted (in the cycle notation) as .
Example: If the function given by
is a transposition.
One of the main results on symmetric groups states that any permutation can be expressed as composition (product) of transpositions, and for any two decompositions of a given permutation, the number of transpositions is always even or always odd.
|Date of creation||2013-03-22 12:24:30|
|Last modified on||2013-03-22 12:24:30|
|Last modified by||drini (3)|