Odd Permutation/Examples/321

Example of Odd Permutation

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

Proof

The permutation $\tuple {1 3}$ transforms $\tuple {1, 2, 3}$ to $\tuple {3, 2, 1}$.

That is $1$ transposition, which is an odd integer.

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): odd permutation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): odd permutation