To that end, you're doing two loops: one from 1 to 7 (call this X) and the other from X+1 to 7.

for $x (1 .. 7) {
  for $y ($x+1 .. 7) {
    push @pairs, [$x,$y];
  }
}
[download]

Update: by "be trickier", I mean, there is also a discernable pattern to the data set in the sequence you've shown. It's not X = (1 .. 7), Y = (X+1 .. 7), it's something else. It's up to you to recognize the pattern. I'll do the hard part for you:

for $x (? .. ?) {
  for $y (? .. ?) {
    push @pairs, [$y, $y-$x];
  }
}
[download]

$N = 6;
for $i (reverse(1..$N)){
    for $j (1..$i){
    print "$j,",$j+1-$i+$N,",";
    }
    print "\b\n";
}
[download]

my $n=7;
for my $a ( 1.. $n-1){
    for( my $b = 1; $b+$a <= $n; $b++){
        print $b, ',', $b+$a, ' ';
    }
    print "\n";
}
[download]

ah, this is more perlish:

my $n=7;
for my $a ( 1..$n-1){
    print $_, ',', $_+$a, ' ' for (1..$n-$a);
    print "\n";
}
[download]

Maybe this one is more "perlish" but the first one you posted is certainly easier to read!

If you are willing to take a little skewed view on the "triangle", it can also be written as:

1,2
1,3 2,3
1,4 2,4 3,4
1,5 2,5 3,5 4,5
1,6 2,6 3,6 4,6 5,6
1,7 2,7 3,7 4,7 5,7 6,7
[download]

Now former diagonals form lines/rows and in this presentation "x" is constant in columns and "y" is constant in rows.

The above output can be generated e. g. by the following obfu code oneliner:
Win command line here; change delimiter from double- to single-quotes for other shell, if applicable

perl -Mstrict -wle "$.++;print qq(@{[map qq{$_,$.}, 1..++$.-1]}) while $.<7"

I'm suppose i'm late :'( ...

Japhy solution solves the problem in a very smart way, i like it too much.

But I have written another (before read any solution ^_^), i put it here for the collection :-)

$max = 7;
for ($i=1; $i<$max; $i++) {
        @tuple = (0,$i);
        print ++$tuple[0],',',++$tuple[1],' ' while ($tuple[1] < $max)
+;
        print "\n"
}
[download]

for ($M=7, $i=1; @_ = (0,$i), $i<$M; $i++)
        { print ++$_[0],',',++$_[1],($_[1]==$M?"\n":" ") while ($_[1] 
+< $M) }
[download]

turo