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| 1 | Surjective |
| 1 | Product |
| 1 | Function |
| 1 | Finite |
| 1 | Even Number |
| 1 | Indexing Set |
| 1 | Relation Theory |
| 1 | Number |
| 1 | Bijection |
| 1 | Permutation |
| 2 | Complimentary |
| 2 | Quantum Logic |
| 3 | Symmetric Group |
| 9 | Cycle Notation |
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Transposition
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
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.