PermutationProblems

PermutationProblems - Quiz 1 Practice Problems:...

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Quiz 1 Practice Problems: Permutations Math 332, Spring 2010 These are not to be handed in. The quiz will be on Tuesday. 1. Write each of the following permutations as a product of disjoint cycles: a. ± 1 2 3 4 5 6 7 8 2 3 4 5 1 7 8 6 ² b. ± 1 2 3 4 5 6 7 8 1 3 8 7 6 5 2 4 ² . 2. Compute each of the following products: a. (1 2 3 5)(4 1 3) b. (1 3 2 5 6)(2 3)(4 6 5 1 2) c. (1 2)(1 3)(2 3)(1 4 2) 3. What is the order of each of the following permutations? a. (1 2 4)(3 5 7) b. (1 2 4)(3 5 6 7) c. (1 2 4)(3 5) d. (1 2 4)(3 5 7 8 6 9) e. (1 2 3 4 5 6 7 8 9)(10 11 12 13 14 15) 4. What is the order of each of the following permutations? a. ± 1 2 3 4 5 6 2 1 5 4 6 3 ² b. ± 1 2 3 4 5 6 7 7 6 1 2 3 4 5 ² 5. Given that α = (1 7 5 2 4 8)(3 9) and β = (2 4 9 8 3 7 5), compute each of the following: a. αβ b. α - 1 c. β 30 d. α 40 . 6. Let β S 7 and suppose β 4 = (1 4 3 5 6 7 2). Find β . 7. Find three elements σ in S 9 with the property that σ 3 = (1 5 7)(2 8 3)(4 6 9). 8.
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PermutationProblems - Quiz 1 Practice Problems:...

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