EXAMPLE (6)
===========
Maple calculations for vector partitions of 4 and their crank mod 5

==============================================================================
>  read "FUNCS.txt":
>  V:=vecptns(4);
>  m:=matrix(nops(V),3):
>  for i from 1 to nops(V) do
>     m[i,1]:=V[i]:
>     m[i,2]:=vpw(V[i]):
>     m[i,3]:=vpcrank(V[i]):
>  od:
>  #Table of vector partitions of 4 with weight and crank
>  print(m);
                      [[[], [], [1, 1, 1, 1]]     1    -4]
                      [                                  ]
                      [ [[], [], [1, 1, 2]]       1    -3]
                      [                                  ]
                      [   [[], [], [2, 2]]        1    -2]
                      [                                  ]
                      [   [[], [], [1, 3]]        1    -2]
                      [                                  ]
                      [    [[], [], [4]]          1    -1]
                      [                                  ]
                      [ [[], [1], [1, 1, 1]]      1    -2]
                      [                                  ]
                      [  [[], [1], [1, 2]]        1    -1]
                      [                                  ]
                      [    [[], [1], [3]]         1     0]
                      [                                  ]
                      [ [[], [1, 1], [1, 1]]      1     0]
                      [                                  ]
                      [  [[], [1, 1], [2]]        1     1]
                      [                                  ]
                      [  [[], [2], [1, 1]]        1    -1]
                      [                                  ]
                      [    [[], [2], [2]]         1     0]
                      [                                  ]
                      [ [[], [1, 1, 1], [1]]      1     2]
                      [                                  ]
                      [  [[], [1, 2], [1]]        1     1]
                      [                                  ]
                      [    [[], [3], [1]]         1     0]
                      [                                  ]
                      [[[], [1, 1, 1, 1], []]     1     4]
                      [                                  ]
                      [ [[], [1, 1, 2], []]       1     3]
                      [                                  ]
                      [   [[], [2, 2], []]        1     2]
                      [                                  ]
                      [   [[], [1, 3], []]        1     2]
                      [                                  ]
                      [    [[], [4], []]          1     1]
                      [                                  ]
                      [ [[1], [], [1, 1, 1]]     -1    -3]
                      [                                  ]
                      [  [[1], [], [1, 2]]       -1    -2]
                      [                                  ]
                      [    [[1], [], [3]]        -1    -1]
                      [                                  ]
                      [  [[1], [1], [1, 1]]      -1    -1]
                      [                                  ]
                      [   [[1], [1], [2]]        -1     0]
                      [                                  ]
                      [  [[1], [1, 1], [1]]      -1     1]
                      [                                  ]
                      [   [[1], [2], [1]]        -1     0]
                      [                                  ]
                      [ [[1], [1, 1, 1], []]     -1     3]
                      [                                  ]
                      [  [[1], [1, 2], []]       -1     2]
                      [                                  ]
                      [    [[1], [3], []]        -1     1]
                      [                                  ]
                      [  [[2], [], [1, 1]]       -1    -2]
                      [                                  ]
                      [    [[2], [], [2]]        -1    -1]
                      [                                  ]
                      [   [[2], [1], [1]]        -1     0]
                      [                                  ]
                      [  [[2], [1, 1], []]       -1     2]
                      [                                  ]
                      [    [[2], [2], []]        -1     1]
                      [                                  ]
                      [  [[1, 2], [], [1]]        1    -1]
                      [                                  ]
                      [    [[3], [], [1]]        -1    -1]
                      [                                  ]
                      [  [[1, 2], [1], []]        1     1]
                      [                                  ]
                      [    [[3], [1], []]        -1     1]
                      [                                  ]
                      [   [[1, 3], [], []]        1     0]
                      [                                  ]
                      [    [[4], [], []]         -1     0]

> 
>  #Total weight of vector partitions of 4
> 
>  add(vpw(V[i]),i=1..nops(V));
                                       5
>  nops(V);
                                       41

> #There are 41 vector partitions of 4 with total weight 5
  #which is p(4).

> 
> 
>  # vector partitions of 4 with crank = 0 mod 5
> 
>  V0:=vecptnsC(4,0,5);
V0 := [[[], [1], [3]], [[], [1, 1], [1, 1]], [[], [2], [2]], [[], [3], [1]],

    [[1], [1], [2]], [[1], [2], [1]], [[2], [1], [1]], [[1, 3], [], []],

    [[4], [], []]]

>  nops(V0);
                                       9

>  add(vpw(V0[i]),i=1..nops(V0));
                                       1

> 
>  # There are 9 vector partitions of 4 with crank = 0 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 1 mod 5
> 
>  V1:=vecptnsC(4,1,5);
V1 := [[[], [], [1, 1, 1, 1]], [[], [1, 1], [2]], [[], [1, 2], [1]],

    [[], [4], []], [[1], [1, 1], [1]], [[1], [3], []], [[2], [2], []],

    [[1, 2], [1], []], [[3], [1], []]]

>  nops(V1);
                                       9

>  add(vpw(V1[i]),i=1..nops(V1));
                                       1

> 
>  # There are 9 vector partitions of 4 with crank = 1 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 2 mod 5
> 
>  V2:=vecptnsC(4,2,5);
V2 := [[[], [], [1, 1, 2]], [[], [1, 1, 1], [1]], [[], [2, 2], []],

    [[], [1, 3], []], [[1], [], [1, 1, 1]], [[1], [1, 2], []],

    [[2], [1, 1], []]]

>  nops(V2);
                                       7

>  add(vpw(V2[i]),i=1..nops(V2));
                                       1

> 
>  # There are 7 vector partitions of 4 with crank = 0 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 3 mod 5
> 
>  V3:=vecptnsC(4,3,5);
V3 := [[[], [], [2, 2]], [[], [], [1, 3]], [[], [1], [1, 1, 1]],

    [[], [1, 1, 2], []], [[1], [], [1, 2]], [[1], [1, 1, 1], []],

    [[2], [], [1, 1]]]

>  nops(V3);
                                       7

>  add(vpw(V3[i]),i=1..nops(V3));
                                       1

> 
>  # There are 7 vector partitions of 4 with crank = 3 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 4 mod 5
> 
>  V4:=vecptnsC(4,4,5);
V4 := [[[], [], [4]], [[], [1], [1, 2]], [[], [2], [1, 1]],

    [[], [1, 1, 1, 1], []], [[1], [], [3]], [[1], [1], [1, 1]], [[2], [], [2]],

    [[1, 2], [], [1]], [[3], [], [1]]]

>  nops(V4);
                                       9

>  add(vpw(V4[i]),i=1..nops(V4));
                                       1

> 
>  # There are 9 vector partitions of 4 with crank = 4 mod 5
>  # and total weight = 1.
> 

==============================================================================

 We see that

 NV(0,5,4)=NV(1,5,4)=NV(2,5,4)=NV(3,5,4)=NV(4,5,4)=1=p(4)/5