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MathGroup Archive 2007

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Re: Riddle with Ordering

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77947] Re: [mg77904] Riddle with Ordering
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 20 Jun 2007 05:34:59 -0400 (EDT)
  • References: <200706191044.GAA07379@smc.vnet.net>

On 19 Jun 2007, at 19:44, nazdrovje at gmail.com wrote:

> Just a gem I discovered with Ordering[ ].
>
> Anyone have an idea what
>
> SomeArrayWithUniqueReals // Ordering // Ordering
>
> does?
>
> I like this, especially the double use of Ordering. Answer tomorrow.
>

Iit's not much of a riddle for anyone who has been reading carefully  
this forum for a while as it has turned up more than once.  It gives  
you the permutation which will turn Sort[AnyList] into AnyList.   In  
other words:

Sort[AnyList][[Ordering[Ordering[AnyList]]]] == Anylist


This means, in particular, that if AnyPermuation is any permutation:

Ordering[Ordering[AnyPermuation]]==AnyPermutation

Moreover, AnyList does not have to be a list of reals, or even a list  
of numbers, and its elements need not be distinct.

Andrzej Kozlowski




  


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