I'm not at all sure I understand your requirement. The query you mention suggests that the easiest thing to do would be to keep the original string along with any transformations. Here's my stab at it.

use 5.026;
use warnings;

use Data::Dumper;

my @strings = qw{
   aaaaaaaaabababacbbbbbbbaccaabc
   aaaaaaaaaaaaaaaaacbbbbbbbaaaca
   aaaaaaaaabaaaaabbaaaaabaaccccc
   };

homogenise( \ @strings );
print Data::Dumper->Dumpxs( [ \ @strings ], [ qw{ *strings } ] );

sub homogenise
{
    my $raStrings = shift;
    my $len       = length $raStrings->[ 0 ];

    foreach my $string ( @{ $raStrings } )
    {
        $string = { original => $string };
        $string->{ byLine } =
           join q{},
           sort split m{}, $string->{ original };
    }

    my $allSorted =
       join q{},
       sort map { split m{}, $_->{ original } } @{ $raStrings };
    my $idx = 0;
    $raStrings->[ $idx ++ ]->{ bySet } = $_
       for unpack qq{(a$len)*}, $allSorted;
}
[download]

The output.

@strings = (
             {
               'bySet' => 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa',
               'original' => 'aaaaaaaaabababacbbbbbbbaccaabc',
               'byLine' => 'aaaaaaaaaaaaaaabbbbbbbbbbbcccc'
             },
             {
               'byLine' => 'aaaaaaaaaaaaaaaaaaaaabbbbbbbcc',
               'original' => 'aaaaaaaaaaaaaaaaacbbbbbbbaaaca',
               'bySet' => 'aaaaaaaaaaaaaaaaaaaaaaaaaaabbb'
             },
             {
               'byLine' => 'aaaaaaaaaaaaaaaaaaaaabbbbccccc',
               'bySet' => 'bbbbbbbbbbbbbbbbbbbccccccccccc',
               'original' => 'aaaaaaaaabaaaaabbaaaaabaaccccc'
             }
           );
[download]

I hope that this is vaguely in the direction you are wanting to go.

---

---

Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!

Titles consisting of a single word are discouraged, and in most cases are disallowed outright.

Read Where should I post X? if you're not absolutely sure you're posting in the right place.

Please read these before you post! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

Posts may use any of the Perl Monks Approved HTML tags:

a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr

You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

	For:		Use:
	&		&
	<		&lt;
	>		&gt;
	[		&#91;
	]		&#93;

Link using PerlMonks shortcuts! What shortcuts can I use for linking?

See Writeup Formatting Tips and other pages linked from there for more info.