my $given = $ARGV[0];
# ...
while (<$dict_fh>) {
    chomp;
    print "$_\n" if is_subset($_, $given);
}
sub is_subset {
    my ($str1, $str2) = @_;
    my (%h1, %h2);
    $h1{$_}++ for split //, $str1;
    $h2{$_}++ for split //, $str2;
    for my $chr (keys %h2) {
        return if ! $h1{$chr} || $h2{$chr} > $h1{$chr};
    }
    return 1;
}

##</code><code>##

my $input = $ARGV[0];
$input = str2val($input);
# dictionary already pre-processed
# create hash of possible subset values
# ...
while (<$dict_fh>) {
    chomp;
    my ($word, $val) = split /\t/;
    print "$word\n" if $is_subset{$input - $val};
}

##</code><code>##

a = 1
b = (a * max) + 1
c = (b * max) + 1
...
z = (y * max) + 1

##</code><code>##

sub str2val {
    my ($str) = @_;
    my %convert = (A => 1, B => 6, C => 31, D => 156, E => 781, F => 3906);
    my $val = 0;
    for my $char (split //, $str) {
        $val += $convert{$char};
    }
    return $val;
}

sub val2str {
    my ($val) = @_;
    my %convert = (A => 1, B => 6, C => 31, D => 156, E => 781, F => 3906);
    my $str = '';
    return $str if $val < 1;
    for my $char (sort {$convert{$b} <=> $convert{$a}} keys %convert) {
        my $count = int($val / $convert{$char});
        $str .= ($char x $count);
        $val %= $convert{$char};
    }
    return $str;
}

##</code><code>##

my $input = $ARGV[0];
my %is_subset = map {$_ => 1} powerset(split //, $input);
while (<$dict_fh>) {
    chomp;
    my ($word, $normalized) = split /\t/;
    print $word if $is_subset{$normalized};
}
sub powerset {
    # ...
    return map {join '', sort @$_} @subsets;
}