Since 132 only took one transposition well call 132

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Unformatted text preview: to 312, and two is even, we’ll say that 312 is an even permutation. Since 132 only took one transposition, we’ll call 132 an odd permutation. Note that a transposition takes any two numbers in the list, and they switch places. We could restrict ourselves to only transposing adjacent numbers in the list, since any transposition is a combination of an odd number of adjacent transpositions. For example, consider the list (9) 12345, and I want to transpose the 2 and 5. It’ll take three adjacent transpositions to get the 2 to the end (10) 12345 → 13245 → 13425 → 13452, and then two more adjacent transpositions to the 5 into the second spot (11) 13452 → 13542 → 15342. Note that both the 2 and 5 have to jump over the 3 and 4, that’s even. And then the 5 and 2 have to switch places, which makes it odd. There are an infinite number of ways to get from one permutation to ano...
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This document was uploaded on 04/03/2014.

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