a) Compute the parity of the n-cycle (1 2 3 ...n). b) Show that a and Baß-1 have the same parity for all permutations a, 3. c) Compute the parity of an arbitrary n-cycle. d) Compute the parity of an arbitrary permutation given the length of the cycles appearing when it is written as a product of disjoint cycles.

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Exercise 10.3.
a) Compute the parity of the n-cycle (1 2 3 ...n).
b) Show that a and ßaß-¹ have the same parity for all permutations a, 3.
c) Compute the parity of an arbitrary n-cycle.
d) Compute the parity of an arbitrary permutation given the length of the cycles
appearing when it is written as a product of disjoint cycles.
Transcribed Image Text:Exercise 10.3. a) Compute the parity of the n-cycle (1 2 3 ...n). b) Show that a and ßaß-¹ have the same parity for all permutations a, 3. c) Compute the parity of an arbitrary n-cycle. d) Compute the parity of an arbitrary permutation given the length of the cycles appearing when it is written as a product of disjoint cycles.
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