Cyclic Permutations: εijk, Even or Odd?

AI Thread Summary
The discussion centers on the properties of the permutation symbol εijk and the classification of cyclic permutations as even or odd. It is established that cyclic permutations like 123 to 231 to 312 are always even, resulting in ε123=ε231=ε312=+1. However, confusion arises regarding the classification of ε132, ε213, and ε321, which are identified as odd permutations with a value of -1. The key point of contention is the assertion in textbooks that all cyclic permutations are even, despite the examples provided showing otherwise. The conversation highlights the need for clarity in understanding the definitions and classifications of permutations in mathematical contexts.
Karol
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εijk is the permutation symbol and cyclic permutations, for example 123→231→312, are always even, thus ε123=ε231=ε312=+1, but:
ε132=ε213=ε321=-1
I understand the first 2, but ε321 is even, no? and also all this series is cyclic, it's not all even and...
 
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Why would ##\varepsilon_{321}## be even?
 
micromass said:
Why would ##\varepsilon_{321}## be even?
Oh sorry, right, but my original question is why is it written in a textbook that every cyclic permutation is even while the cyclic permutations ε132=ε213=ε321 are odd?
 

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