brute:

 (1/8 * D_{m}{F_{n p}} * V_{q} 
+ 1/8 * D_{n}{F_{m p}} * V_{q} 

- 1/8 * D_{m}{F_{n q}} * V_{p} 
- 1/8 * D_{m}{F_{p n}} * V_{q} 
+ 1/8 * D_{m}{F_{p q}} * V_{n} 
+ 1/8 * D_{m}{F_{q n}} * V_{p} 
- 1/8 * D_{m}{F_{q p}} * V_{n} 

- 1/8 * D_{n}{F_{m q}} * V_{p} 
- 1/8 * D_{p}{F_{m n}} * V_{q} 
+ 1/8 * D_{p}{F_{m q}} * V_{n} 
+ 1/8 * D_{q}{F_{m n}} * V_{p} 
- 1/8 * D_{q}{F_{m p}} * V_{n});

smart:

 (1/4 * D_{m}{F_{n p}} * V_{q} 
+ 1/8 * D_{n}{F_{m p}} * V_{q} 

- 1/4 * D_{m}{F_{n q}} * V_{p} 
+ 1/4 * D_{m}{F_{q n}} * V_{p}  vs  D_{m}{F_{p q}} V_{n}

- 1/8 * D_{n}{F_{m q}} * V_{p} 
- 1/8 * D_{p}{F_{m n}} * V_{q} 
+ 1/8 * D_{p}{F_{m q}} * V_{n} 
+ 1/8 * D_{q}{F_{m n}} * V_{p} 
- 1/8 * D_{q}{F_{m p}} * V_{n});

The boxes are isolated correctly.
The implicit antisymmetry of the original tensor is found correctly.
And even the combinatorics output is correct:

1 0 2 3 
1 0 3 2 
3 0 1 2 

Nevertheless, the permutation with 1/4 prefactors is not correct.

Is this really correct?:

			src_fd+=sym[i][j];
			dst_fd+=sym.original[j];

If this is, can we use different sublengths to achieve what we want?
 
_   _
1 0 2 3  ->  1 0 2 3    D_{m}{F_{n p}} V_{q}
1 0 3 2 		 1 0 3 2    D_{m}{F_{n q}} V_{p}
3 0 1 2 		 2 0 3 1    D_{m}{F_{p q}} V_{n}

Yes, this works of course. Interesting duality: sublength blocks are
for permutation by location what input_asym is for permutation by
value.

 n m
 p 
 q

A:=  1/24 * V_{m n} * F_{p q} 

   - 1/24 * V_{m n} * F_{q p} 

   - 1/24 * V_{m p} * F_{n q} 
   + 1/24 * V_{m p} * F_{q n} 

   + 1/24 * V_{m q} * F_{n p} 
   - 1/24 * V_{m q} * F_{p n} 
   - 1/24 * V_{n m} * F_{p q} 
   + 1/24 * V_{n m} * F_{q p} 
   + 1/24 * V_{n p} * F_{m q} 
   - 1/24 * V_{n p} * F_{q m} 
   - 1/24 * V_{n q} * F_{m p} 
   + 1/24 * V_{n q} * F_{p m} 
   + 1/24 * V_{p m} * F_{n q} 
   - 1/24 * V_{p m} * F_{q n} 
   - 1/24 * V_{p n} * F_{m q} 
   + 1/24 * V_{p n} * F_{q m} 
   + 1/24 * V_{p q} * F_{m n} 
   - 1/24 * V_{p q} * F_{n m} 
   - 1/24 * V_{q m} * F_{n p} 
   + 1/24 * V_{q m} * F_{p n} 
   + 1/24 * V_{q n} * F_{m p} 
   - 1/24 * V_{q n} * F_{p m} 
   - 1/24 * V_{q p} * F_{m n} 
   + 1/24 * V_{q p} * F_{n m};

B:= V_{m n} * F_{p q} 

  - V_{m p} * F_{n q} 
  + V_{m q} * F_{n p} 
  + V_{n p} * F_{m q} 
  - V_{n q} * F_{m p} 
  + V_{p q} * F_{m n};


@(A)-@(B):
@canonicalise!(%):
@collect_terms!(%);




