Hello. Needs help with disjoint cycles.

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SUMMARY

The discussion focuses on expressing permutations as products of disjoint cycles, specifically for the permutations (1,2,3)(4,5)(1,6,7,8,9)(1,5) and (1,2)(1,2,3)(1,2). The user seeks guidance on how to perform this without converting to two-row permutations. Additionally, they inquire about determining whether a permutation is odd or even. The conversation highlights the importance of understanding cycle notation and parity in permutations.

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Charles007
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Express as the product of disjoint cycles:
a. (1,2,3)(4,5)(1,6,7,8,9)(1,5)
b. (1,2)(1,2,3)(1,2)


I now how to do in 2 row permutations, with right to - left. can anyone tell me , how to express it without transfer it into 2 row permutations.

One more question, How do we find out it's odd or even permutaions.

Thank you. I am doing my past exam paper, university doesn't give us answer.
 
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