Just a hack but how about the following to get started:

# The @AllPatterns array is probably fed elsewhere, this is just for t
+he test
@AllPatterns = ([qw(1 2 1 1 8)],
        [qw(1 6 5 12 12)],
        [qw(1 1 1 1 1)],
        [qw(1 1 1 1 1)]);

for $v (@AllPatterns) {
    ++$h{join(' ',sort {$a <=> $b} @$v)};
} 

for $k (sort keys %h) { print "$h{$k} - $k\n"; }
[download]

This will probably choke (run out of memory) on a "gigantic array" so you might need to write to disk after each step you outlined.

Update: Just struck me that you may have a simple array rather than a 2D as I has assumed. Possibly clear how to adapt the hack but here it is just to get it out of my head:

@AllPatterns = ('1 2 1 1 8',
        '1 6 5 12 12',
        '1 1 1 1 1',
        '1 1 1 1 1');
for $v (@AllPatterns) {
    ++$h{join(' ',sort {$a <=> $b} split(' ',$v))};
}
[download]

and then print as before.