# Cyclic permutations

1. Aug 17, 2015

### Karol

εijk is the permutation symbol and cyclic permutations, for example 123→231→312, are always even, thus ε123231312=+1, but:
ε132213321=-1
I understand the first 2, but ε321 is even, no? and also all this series is cyclic, it's not all even and....

2. Aug 17, 2015

### micromass

Staff Emeritus
Why would $\varepsilon_{321}$ be even?

3. Aug 17, 2015

### Karol

Oh sorry, right, but my original question is why is it written in a text book that every cyclic permutation is even while the cyclic permutations ε132=ε213=ε321 are odd?