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Number of ways of permutations to form a certain pattern of cycles?
Dear all, How to compute in Mathematica the number of ways of permutations of n- objects to form a certain pattern of cycles? I mean, for example, let n = 3. then there are 6 ways of permutations of three objects 123, 231, 312, 132, 213, 321 Among them, we have the three 1-cycle pattern, 123 two 3-cycle pattern, 231, 312 one 1-cycle and one 2-cycle pattern, 132, 213, 321 How to calculate this kind of mathematical problem with Mathematica? Could you also show me how to calculate the number of ways without using of Mathematica? Thanks so much!