You understand what an array is. If you push an array onto another array, you just wind up with a single bigger single dimensional array. A multi dimensional array is an array of references to array. Push a reference to the @e array onto the @f array. push @f,\@e; I suppose you could write, push @f,[@e], but that would expand @e into an anonymous array and then make a reference to that newly created anon array.

BTW, there can be huge problems if you don't use "my" variables. "my @e" creates a brand new @e array every time this is seen. The push, pushes a reference to the "current @e array". When the loop comes around again, a whole new different @e array is created.

use strict;
use warnings;
use Data::Dump qw(pp);

my @f;
for my $i (0..40) 
{
   my @e=($i+=2, $i+1); #same as ($i+2, $i+3)
   push(@f,\@e); 
}

pp \@f;

__END__
Not sure if this is what you want, but
this code results in:
[
  [2, 3],
  [3, 4],
  [4, 5],
  [5, 6],
  [6, 7],
  [7, 8],
  [8, 9],
  [9, 10],
  [10, 11],
  [11, 12],
  [12, 13],
  [13, 14],
  [14, 15],
  [15, 16],
  [16, 17],
  [17, 18],
  [18, 19],
  [19, 20],
  [20, 21],
  [21, 22],
  [22, 23],
  [23, 24],
  [24, 25],
  [25, 26],
  [26, 27],
  [27, 28],
  [28, 29],
  [29, 30],
  [30, 31],
  [31, 32],
  [32, 33],
  [33, 34],
  [34, 35],
  [35, 36],
  [36, 37],
  [37, 38],
  [38, 39],
  [39, 40],
  [40, 41],
  [41, 42],
  [42, 43],
]
[download]

Update: Now that I think about it, $i+=2 is an extremely bad idea. $i is the loop variable. You are asking for big trouble if you attempt to modify the loop variable while you are within the for loop. It does work here, but in general, I would avoid it and go with my ($i+2, $i+3) formulation.