Chapter 5 Exercise 1 |
| This software determines whether the two permutations (1x) and (123 ... n) generate Sn for various choices of x and n. (That is, whether every element of Sn can be expressed as some product of these permutations. ) For n = 4, run the program for x = 2, 3, and 4. For n = 5, run the program for x = 2, 3, 4, and 5. For n = 6, run the program for x = 2, 3, 4, 5, and 6. For n = 8, run the program for x = 2, 3, 4, 5, 6, 7, and 8. Conjecture a necessary and sufficient condition involving x and n for (1x) and (123 ... n) to generate Sn. |