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Re: Order of Permutations of a Certain ~Kind~ Across the (Odd)
Integers
Posted:
Jan 9, 2013 2:31 PM
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On Tue, 08 Jan 2013 22:28:05 +0100, Timothy Murphy wrote:
> P. Michael Hutchins wrote:
>> A ~kind~ of permutation - call it "inside out" - can be specified for any
>> integer. (I use only the odd ones, for reasons that should become
>> obvious.)
>>
>> For a set of N elements..
>> (which I represent as just a string of integers - eg: 12345)
>>
>> ..the permutation takes: to:
>> o the middle one (N+1/2): 1
>> o the one to the left of that: 2
>> o the one to the right of that: 3
>> ...and so on
>>
>> eg: for 12345, we have:
>>
>> 12345
>> 34251
>> 25413
>> 41532
>> 53124
>> 12345
>>
>> ...so this guy's order is 5.
>
> I cannot follow your example.
> As far as I can see from your description
> 3->1, 2->2, 4->3, 1->4, 5->5,
> ie (1,4,3)(2)(5) with order 3.
>
> I'm assuming that "that" means "the middle one", ie 3.
Hutchins' description seems to have 'left' and 'right' reversed.
A tuple (1, 2, 3 ... 2m-1) permutes to
( m, m+1, m-1, m+2, m-2, m+3 ... 2m-1, 1)
--
jiw
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