Prove the following about S n if n 3. a. Every permutation in S n can
Question:
Prove the following about Sn if n ≥ 3.
a. Every permutation in Sn can be written as a product of at most n - I transpositions.
b. Every permutation in Sn that is not a cycle can be written as a product of at most n - 2 transpositions.
c. Every odd permutation in Sn can be written as a product of 2n + 3 transpositions, and every even permutation as a product of 2n + 8 transpositions.
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a Note that 1 21 2 is the identity permutation in S n and 2 n 1 if n 2 Because 1 2 3 4 n 1 n1 n 1 1 ...View the full answer
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