Update:
Probably a better way to get the index of max value...But is this what you want?
Code should run fairly quickly albeit a bit wordy for Perl.

#!/usr/bin/perl
use strict;
use warnings;


my @array = split '', "117";
print @array, "\n";
print @array,"\n" while rot_max_left(\@array);


@array = split '', "1234";
print "\n",@array,"\n";
print @array,"\n" while rot_max_left(\@array);


sub rot_max_left
{
    my $array_ref = shift;
    
    my $maxi=0;
    return 0 unless ($maxi = get_index_of_max($array_ref));
    
    ($array_ref->[$maxi-1],$array_ref->[$maxi]) = ($array_ref->[$maxi]
+,$array_ref->[$maxi-1]);
    return $maxi;
}

sub get_index_of_max
{
  my $array_ref = shift;
  
  my $maxi = 0;
  foreach (my $i=1;$i<@$array_ref;$i++)
  {
     $maxi = $i if ($array_ref->[$i] > $array_ref->[$maxi])
  }
  return $maxi;
}

__END__
117
171
711

1234
1243
1423
4123
[download]

If you hit the highest digit as the first digit, then:
1. Sorting of remaining digits.
2. if you cannot sort any further, (ie.. it is already in reverse order) than sort from the beginning position. ( to return to the original number. 321 -> 123)

If you want to learn Perl, I would like to see your attempt at this extra behaviour. Then I and the group can help you with that. The general approach here is "post a question", "get some info", "learn and experiment", "post another question based upon what you've learned and your experimentation".

I've given you a start although I probably should have named rot_max_left() as shift_max_left(). I encourage you to give this a go yourself and post your code.

Please note that you can easily implement any "swap" with array slices, like

@a[0,1]=@a[1,0]

and @a=split//,$number

will initialize it.

Now you know everything needed to implement your ideas.

HTH! :)