The major problem with the code you have there is that it doesn't give combinations of separated list items, it only gives items from one point forward. As an example:
for n=3, with items 1,2, and 3, i get the following from your code:
1
1 2
1 2 3
2
2 3
3
Note the missing '1 3' case. For the items 1,2,3, and 4, '134', '124', '13', '14', etc would be missing.

Merlyn's snippets are a nice and easy way to go; a simple transformation and they will return an array of strings instead of an AoA. As an exercise, i chalked up a non-recursive solution as well; it returns an array of arrays as merlyn's does.

sub combinations {
  my (@comb, $pos);
  my $limit = 2**@_;

  while (my $item = shift) {
    my $step = 2**@_;
    for ($pos = 0; $pos < $limit; $pos += $step) {
      push @{$comb[$pos++]}, $item for 1..$step;
    }
  }

  return @comb, [];
}
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