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Unformatted text preview: Name: Solutions Exam 3 Instructions. Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Put your name on each page of your paper. 1. [15 Points] Let fi = 1 2 3 4 5 6 2 1 3 5 4 6 and fl = 1 2 3 4 5 6 6 1 2 4 3 5 . Compute the following permutations: (a) fifl (b) flfi (c) fl 1 I Solution. (a) fifl = 1 2 3 4 5 6 6 2 1 5 3 4 = 1 6 4 5 3 (2) (b) flfi = 1 2 3 4 5 6 1 6 2 3 4 5 = (1) 2 6 5 4 3 (c) fl 1 = 1 2 3 4 5 6 2 3 5 4 6 1 = 1 2 3 5 6 (4) J 2. [12 Points] Let 2 S 10 be the permutation 1 2 3 4 5 6 7 8 9 10 9 7 8 4 3 2 10 5 1 6 : (a) Find the cycle decomposition of . I Solution. = 1 9 2 7 10 6 3 8 5 J (b) Determine if is even or odd. I Solution. is odd since it is the product of two odd and one even permutation. The odd permutations are the 2cycle and the 4cycle, while the 3cycle is even. J 3. [12 Points] How many permutations in S 7 have cycle structure (1...
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 Fall '09

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