Category:Definitions/Even Permutations
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This category contains definitions related to Even Permutations.
Related results can be found in Category:Even Permutations.
Definition
Let $n \in \N$ be a natural number.
Let $S_n$ denote the symmetric group on $n$ letters.
Let $\rho \in S_n$ be a permutation in $S_n$.
Definition 1
$\rho$ is an even permutation if and only if $\rho$ is equivalent to an even number of transpositions.
Definition 2
$\rho$ is an even permutation if and only if:
- $\map \sgn \rho = 1$
where $\sgn$ denotes the sign function.
Examples
Example: $312$
- $\tuple {3, 1, 2}$ is an even permutation of $\tuple {1, 2, 3}$.
Also see
- Results about even permutations can be found here.
Subcategories
This category has the following 3 subcategories, out of 3 total.
D
E
Pages in category "Definitions/Even Permutations"
The following 3 pages are in this category, out of 3 total.