'a{b,c}d{e,fg{,h,ij}k}l{,m{n,o}}';

I suppose that is not a given, but this might guaranty a unique solution.

OTOH if characters can be repeated I'd bet that multiple solutions are possible.

Please clarify.

update

for instance all these glob expressions are equivalent ( I removed the variations where {,a} and {a,} were swapped)

use v5.12;
use warnings;
use Data::Dump;
use Test::More;

test (
      [ <{a,aa}> ],
      [ <{,a}{a}> ],
      [ <{a}{,a}> ],
      [ <a{,a}> ],
      [ <{,a}a> ],
     );

sub test {
    my @g = @_;
    my (%h1,%h2);
    for my $i (0..$#g) {
        for my $j ($i+1..$#g) {
            is_deeply(
                      [sort @{$g[$i]}],
                      [sort @{$g[$j]}],
                      "$i,$j")
              or ddx $g[$i],$g[$j];
        }
    }
}

done_testing;
[download]

you should also add that curlies and commas should be minimal as a second criteria.

for instance a , {a} and {{a}} are all equivalent.

best you provide a sub metric

edit

sub cmp_glob($g1,$g2) which returns -1, 0 or 1 like cmp does.

> for instance a , {a} and {{a}} are all equivalent.

Interestingly, we've found a place where Perl's glob behaves differently to the brace expansion in bash:

$ perl -wE 'say glob "{{a}}"'
a
$ echo {{a}}
{{a}}
[download]

map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]

I tend to side with the shell here. Braces which don't enclose a comma are not a glob pattern (for me).

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