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Explain why every permutation in S(n) can be represented by a product of n-1 or fewer cycles of length 2 (transpositions). Represent the permutationσ in problem (1) above as a product of 8 or fewer tr...

Explain why every permutation in S(n) can be represented by a product of n-1 or fewer cycles of length 2 (transpositions). Represent the permutationσ in problem (1) above as a product of 8 or fewer transpositions. Is σ an even or an odd permuation?

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Theorem 2: Every permutation can be expressed as a composite of disjoint cycles Proof: Let the given permutation f be denoted

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Explain why every permutation in S(n) can be represented by a product of n-1 or fewer cycles of length 2 (transpositions). Represent the permutationσ in problem (1) above as a product of 8 or fewer tr...
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