Is there in general any difference between a cyclic and an even permutation? Or can they be used interchangeably. Is an acyclic permutation the same as an odd permutation?
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2This is false in both directions. Cyclic does not imply even, and even does not imply cyclic. – Dietrich Burde Dec 02 '21 at 16:17
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Is there in general any difference between a cyclic and an even permutation?
Yes.
The permutation $(12)(34)$ is even but not cyclic. The permutation $(1234)$ is cyclic but odd.
Shaun
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