Unformatted text preview: of some number of 2cycles. Hint: For the ﬁrst part, look at your computations in Exercise 1.5.3 to discover the right pattern. Then do a proper proof by induction. 1.5.6. Explain how to compute the inverse of a permutation that is given in twoline notation. Compute the inverse of ± 1 2 3 4 5 6 7 2 5 6 3 7 4 1 ² : 1.5.7. Explain how to compute the inverse of a permutation that is given as a product of cycles (disjoint or not). One trick of problem solving is to simplify the problem by considering special cases. First you should consider the case of a single cycle, and it will probably be helpful to begin with a short cycle. A 2cycle is its own inverse, so the ﬁrst interesting case is that of a 3cycle. Once you have ﬁgured out the inverse for a 3cycle and a 4cycle, you will probably be able to guess the general pattern. Now you can begin work on a product of several cycles....
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 Fall '08
 EVERAGE
 Algebra, Permutations, Multiplication, Symmetric group, multiplication table, equilateral triangular card

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