Definition:Even Permutation/Definition 1

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 $S_n$.

$\rho$ is an even permutation if and only if $\rho$ is equivalent to an even number of transpositions.

Examples

Example: $312$

$\tuple {3, 1, 2}$ is an even permutation of $\tuple {1, 2, 3}$.

Also see

• Equivalence of Definitions of Even Permutation

• Results about even permutations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): even permutation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): even permutation
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): even permutation