In common with others, I'm not sure how this question relates to your OP ([ 3,2,2,3,3,3,1 ] doesn't look like a linked list to me, either), but I can answer your specific questions.

... what exact data type [is] $L ...

$L is a scalar. This is determined by the $ sigil before the symbol.

... how [does] the data set get passed into @_ and assigned to $L.

The expression  [ 3,2,2,3,3,3,1 ] returns a reference (to an array). A reference is always a scalar value even though the referent, e.g., an array or hash, is not. A scalar is passed to a subroutine in the usual way:

c:\@Work\Perl>perl -wMstrict -le
"my $arrayref = [ 3,2,2,3,3,3,1 ];
 ;;
 sub func {
   my ($msg, $ar) = @_;
   ;;
   printf qq{$msg: scalar ref: $ar };
   printf qq{'$_' } for @$ar;
   printf qq{(%d elements) \n}, scalar @$ar;
   }
 ;;
 func('A', [ 9, 8, 7 ]);
 func('B', $arrayref);
"
A: scalar ref: ARRAY(0x1cb226c) '9' '8' '7' (3 elements)
B: scalar ref: ARRAY(0x6fd05c) '3' '2' '2' '3' '3' '3' '1' (7 elements
+)
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Update: Changed code example: added element count. Slight wording change.