Here's mine just to prove I can, but it's much sloppier than most of the examples given here. I'll have to analyze your code and see if I can make mine more efficient.

sub permute {
    return if $_[0] && $_[0] / length($_[0]) != int ($_[0] / length($_
+[0]));
    if (!length($_[1])) { print $_[0]." "; return; }
    for (0..length($_[1])-1) {
         permute($_[0].substr($_[1],$_,1), substr($_[1],0,$_).substr($
+_[1],$_+1));
    }
}
[download]

Incidently, I tried some larger numbers and found that the following are all the matches up through 19 digits:

1 : 1
12 : 12 
123 : 123 321 
123456 : 123654 321654 
12345678 : 38165472 
123456789 : 381654729 
1234567890 : 3816547290
[download]

Then you hit 20 and start getting piles of matches. My algorithm isn't efficient enough yet to go beyond 21 or so.

EDIT:
si_lence gets ~27 iterations per second
Ted_Pride gets ~100 iterations per second
tilly gets ~154 iterations per second