Lecture Notes (19)

Since 132 only took one transposition well call 132

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 04/03/2014.

Ask a homework question - tutors are online