I borrowed this for something and noticed that if $num=8 this produces only 40319 permutations... I made the following el cheapo minor modification on mine.

sub make_orderings
{
   my $num = shift;

   my @arr = (1 .. $num);
   my $first = 1;

   return sub {
      if( $first ) {
          $first = 0;
          return @arr;
      }
      my $last = $#arr;

      my $i = $last - 1;
      $i-- while 0 <= $i && $arr[$i] >= $arr[$i+1];
      return if $i == -1;

      @arr[$i+1..$last] = reverse @arr[$i+1..$last]
         if $arr[$i+1] > $arr[$last];

      my $j=$i+1;
      $j++ while $arr[$i] >= $arr[$j];

      @arr[$i,$j] = @arr[$j,$i];

      return @arr;
   }
}
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