You can't take a reference to a slice. You have to copy. But you can do that with just a slight change of your first program. A one line change (and one char less!)

#!/usr/bin/perl

use strict;
use warnings;

my @list = (0, 1, 2, 3, 4, 5, 6, 7);
print "@list\n";
my @short = @list[1..4];
print "@short\n";
my $ref = [@list[2..4]];   # <---  Change this line.
print "@$ref\n";
__END__
0 1 2 3 4 5 6 7
1 2 3 4
2 3 4
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Abigail