Even Permutation/Examples/312

Examples of Even Permutations

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

Proof

The permutations $\tuple {1 3}$ and then $\tuple {1 2}$ transform $\tuple {1, 2, 3}$ to $\tuple {3, 1, 2}$.

That is two transpositions, which is an even integer.

Hence the result.

$\blacksquare$

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