Can you comment on this by which logic the first for conditions are set ( 0 .. $#lt -1 ) also the combination $# I have not encountered something like this what does it mean?

Absolutely. That's what this place is all about.

[
    [1], 
    [2, 3], 
    [4, 5, 6], 
    [7, 8, 9, 10]
]
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### $#array is the highest index in @array.
my $yMax = $#lt; 

## $#{ ... } is the highest index in the array referenced by ...
## $array[ -1 ] is the last element in the @array
## So the following sets $xMax to highest index of the array (referenc
+e)
## in the last element of @lt. Ie. The longest subarray.

my $xMax = $#{ $lt[-1] };

## Iterate through each the subarrays except the last which does need 
+padding
for my $y ( 0 .. $yMax -1 ) {
    
    ## for $lt[ $y=0 ] ([1]),    we need to add elements $y+1..$xMax (
+1..3)
    ## for $lt[ $y=1 ] ([2,3]),  we need to add elements $y+1..$yMax (
+2..3)
    ## And the value we add at $lt[ $y ][ $x ] comes from $lt[ $x ][ $
+y ].

    for my $x ( $y+1 .. $xMax )
        push @{ $lt[ $y ] }, $lt[ $x ][ $y ];
    }
}
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BTW: please use <code></code> tags when posting code snippets. That way they are readable :)