TIMTOWTDI

use Algorithm::Combinatorics qw/combinations/;
use strict;
use warnings;

use constant DEBUG => 0;
use constant ALL => 1;

local $\ = "\n"; # UPDATE#1 = I was using perl -l to run; if you don't
+, you'll want this...


my @array = qw(2 6 5 7 4 3 9);
my $Fcount = @array;
my @answer = ();
while( $Fcount ) {
    my $iter = combinations( \@array, $Fcount );
    while( my $p = $iter->next() ) {
        my $monotonic = 1;
        my @a = @$p;
        foreach my $i ( 0.. $#a-1 ) {
            my $j = $i + 1;
            $monotonic &&= $a[$j] > $a[$i];
            last unless $monotonic;
        }
        push @answer, [@a] if $monotonic;
        $monotonic ||= 0; # not necessary, except it cleans up my debu
+g print
        print "$Fcount: (@a): $monotonic || (@answer)"  if DEBUG;
        last if $monotonic && !ALL; # this could also be 'last if @ans
+wer && !ALL;'
    }
    --$Fcount;
    last if @answer && !ALL;
}
foreach my $p (@answer) {
    local $, = "\t";
    local $" = ",";
    print scalar(@$p), "(@$p)";
}

__END__
4       (2,6,7,9)
4       (2,5,7,9)
3       (2,6,7)
3       (2,6,9)
3       (2,5,7)
3       (2,5,9)
3       (2,7,9)
3       (2,4,9)
3       (2,3,9)
3       (6,7,9)
3       (5,7,9)
2       (2,6)
2       (2,5)
2       (2,7)
2       (2,4)
2       (2,3)
2       (2,9)
2       (6,7)
2       (6,9)
2       (5,7)
2       (5,9)
2       (7,9)
2       (4,9)
2       (3,9)
1       (2)
1       (6)
1       (5)
1       (7)
1       (4)
1       (3)
1       (9)
[download]

change to ALL => 0 to get just the first combination that's increasing.

update: added $\ = "\n";

update 2 (2016-Oct-24): please don't use this code in production; it is highly inefficient. see Re^7: Longest Increasing Subset