I'm not sure if the braces around the zero have any effect.

Then find it out:

use Data::Dumper;
# your initialization code here
print Dumper \%hash;
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About your other questions:

$hash{"LISTS"}=[() x $length]

This doesn't do what you want, since you want really references to empty arrays, not empty lists (which get flattened out).

# WRONG
$hash{"LISTS"}=[([]) x $length]
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won't work either, because it returns many references to the same array.

A working solution is

$hash{LISTS} = [ map [], 1..$length ];
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Though often this is not needed at all, thanks to autovivification. This works without error:

my %hash;

# automatically creates $hash{LISTS} as an array ref,
# and $hash{LISTS}[3] as an array ref:
push @{$hash{LISTS}[3]}, 'new item';

# also works for direct assignment:
$hash{LISTS}[4][0] = 'other new item';
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