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>  # @p is the position of each element in @o,
>  # that is, @o = (0..$#e)[@p]
>  my @p= (0..$#e);
>  # Note that it is also true that @p = (0..$#e)[@o].

  # an arbitrary permutation
  @o = @permutation = (1,2,0);
...
  @p = @positions   = (2,0,1); 
  # And then 
  print " o[p] = (@o[@p]) = p[o] = (@p[@o]) \n";

 o[p] = (0 1 2) = p[o] = (0 1 2)