#!/usr/bin/perl
use warnings;
use strict;

my %fragments = ( 1 => { F => 'TTAAGTAGCATCGATTTATAGCATCGACTAGTAA',
                         R => 'TTACTAGTCGATGCTATAAATCGATGCTACTTAA',
                       },
                  2 => { F => 'TTAGCTACGATCAGCTACGATCGAGCGACTACGTAGCAA
+',
                         R => 'TTGCTACGTAGTCGCTCGATCGTAGCTGATCGTAGCTAA
+',
                       },
                );

my %combinations;

for my $fragment (keys %fragments) {
    for my $other_fragment (keys %fragments) {
        next if $fragment eq $other_fragment;
        for my $cognate (qw( F R )) {
            for my $other_cognate (qw( F R )) {
                $combinations{"$fragment$cognate$other_fragment$other_
+cognate"}
                    = $fragments{$fragment}{$cognate}
                    . $fragments{$other_fragment}{$other_cognate};
            }
        }
    }
}

use Data::Dumper;
print Dumper(\%combinations);
[download]

This generates 8 entries, not four, as it creates 2F1F etc., too. You can modify the "next" condition to avoid it, i.e.

        next if $fragment ge $other_fragment;
[download]

If you need to combine N fragments, see Algorithm::Loops.

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]