my %HoHoA = (
              'set1' => {
                         'key1_set1' => [ 'some arrays' ],
                         'key2_set1' => [ 'some arrays' ],
                       },

              'set2' => {
                         'key1_set2' => [ 'some arrays' ],
                         'key2_set2' => [ 'some arrays' ],
                       },

              'set3' => {
                         'key1_set3' => [ 'some arrays' ],
                         'key2_set3' => [ 'some arrays' ],
                       },

              'set4' => {
                         'key1_set4' => [ 'some arrays' ],
                         'key2_set4' => [ 'some arrays' ],
                         'key3_set4' => [ 'some arrays' ],
                       },

);


##</code><code>##

key1_set1 - key1_set2
key1_set1 - key2_set2
key1_set1 - key1_set3
key1_set1 - key2_set3
key1_set1 - key1_set4
key1_set1 - key2_set4
key1_set1 - key3_set4
key2_set1 - key1_set2
key2_set1 - key2_set2
key2_set1 - key1_set3
key2_set1 - key2_set3
key2_set1 - key1_set4
key2_set1 - key2_set4
key2_set1 - key3_set4
...
key1_set3 - key1_set4
key1_set3 - key2_set4
key1_set3 - key3_set4
key2_set3 - key1_set4
key2_set3 - key2_set4
key2_set3 - key3_set4

##</code><code>##

foreach my $set ( sort keys %HoHoA)
{
    print "$set\n";
    my @key = keys %{$HoHoA{$set}};

    for ( my $i = 0; $i<@key; $i++ )
    {
        for (my $j=$i+1; $j<@key; $j++  )
        {
           print "$key[$i] - $key[$j]\n";
        }
    }
}
# Am I attacking the problem correctly?