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Let $\sigma \in S_4$ be the permutation that sends $(a,b,c,d) \to (b,d,a,c).$ Then the cycle notation is $(1342)=(23)(34)(12).$

But if we denote $a$ as $1,$ $b$ as $2$, $c$ as $3$ and $d$ as $4,$ then it means $\sigma(1)=2, \sigma(2)=4, \sigma(3)= 1$ and $\sigma(4)=3.$ Hence, isnt the cycle notation $(1243)$ instead?

Kindly advise, thank you.

Alexy Vincenzo
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  • You have found the two different interpretations of cycle notation. Some authors use one, some use the other. As long as whoever is writing makes it clear at the start how to interpret cycles, there's no harm done. – Gerry Myerson Nov 07 '19 at 04:20
  • By the way, the way I learned to do cycle multiplication, $(23)(34)(12)=(1243)$. – Gerry Myerson Nov 07 '19 at 04:21

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