- #1

catherinenanc

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1. I think my professor gave me credit for this problem when he shouldn't have! I just want to understand for the test, so I want someone to verify for me.

2. How do you find out whether a given permutation is even or odd without factoring it into transpositions?

3. My answer was:

Factor it into disjoint cycles (not necessarily 2-cyles, or transpositions).

Count the number of even cycles (those with an odd r).

If this count is even, the permutation is even. If this count is odd, then the permutation is odd.

but in looking back over my work to study for the test, I think it should have been:

Factor it into disjoint cycles (not necessarily 2-cyles, or transpositions).

Count the number of

If this count is even, the permutation is even. If this count is odd, then the permutation is odd.

Am I right in doubting my previous answer?

2. How do you find out whether a given permutation is even or odd without factoring it into transpositions?

3. My answer was:

Factor it into disjoint cycles (not necessarily 2-cyles, or transpositions).

Count the number of even cycles (those with an odd r).

If this count is even, the permutation is even. If this count is odd, then the permutation is odd.

but in looking back over my work to study for the test, I think it should have been:

Factor it into disjoint cycles (not necessarily 2-cyles, or transpositions).

Count the number of

*cycles (those with an*__odd__*r).*__even__If this count is even, the permutation is even. If this count is odd, then the permutation is odd.

Am I right in doubting my previous answer?

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