But you can setup almost-autovivification if you want it, however it's not as transparent as in Perl. The Hash.new method can take a block which is passed the instance and the missing key when you try and access a non-existent key. So if you wanted to have it autovivify with an Array instance you do something like:

h = Hash.new { |h,k| h[k] = Array.new }
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Similarly Array.new has a block initializer which will let you pre-fill it with a computed value (although it is missing something analogous to the Hash version mentioned above; then again there's nothing to stop you from extending the builtin Array class to do so either; in fact you might even could use reflection to see if the block takes one or two arguments and emulate the old behavior as well).

Update: And yes, this is very different from the Perl case. Ruby is relying on explicit instructions from the programmer rather than syntactic hints (which I think is what you were getting at, rather than saying you absolutely can't do it in Ruby).