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January 28th, 2012, 12:42 AM  #1 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  find an inverse of a permutation cycle
Find an inversion of the following cycle How do we do that?? 
January 28th, 2012, 01:58 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: find an inverse of a permutation cycle
just write the numbers in reverse order, so the inverse is (341) http://www.math.csusb.edu/notes/advance ... node9.html 
January 29th, 2012, 12:48 AM  #3 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  Re: find an inverse of a permutation cycle
that is very strange because for example in my book the author gives such examples (123) has an inverse (132) and (132) has an inverse (123) and (135) has (153) so it seems that the only numbers that change their places are the middle one and the last one.... 
January 29th, 2012, 01:33 AM  #4  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: find an inverse of a permutation cycle Quote:
To find the inverse of a permutation that is a cycle all we have to do is write the elements of the cycle in reverse order. Thus the inverse of (1 2 3 4) is (4 3 2 1). Since a cycle can be written with any of its elements as the first term we can also write this inverse as (1 4 3 2). This gives an alternative way to write down the inverse of a cycle. Fix the first element in the cycle and write the remaining elements in reverse order. Thus, the inverse of (1 2 3 4 5) is (1 5 4 3 2).  
January 29th, 2012, 01:50 AM  #5 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  Re: find an inverse of a permutation cycle
ah okej, finally I got it So it does not matter which order I take then for ex right? or right? and for the original post ok? 
January 29th, 2012, 02:26 AM  #6  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: find an inverse of a permutation cycle Quote:
 

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