FUNCTION:  partitions[vecptns] - generate vector partitions
 
CALLING SEQUENCE:  vecptns(n)
 
PARAMETERS:     n  -  positive integer
 
GLOBAL VARIABLES: NONE                

SYNOPSIS:  
   Generates a list of vector-partitions of n.
   A vector partitions is an element of DP x P x P
   where DP is the set of partitions into distinct parts, and
          P is the set of unrestricted partitions 
EXAMPLES:  
                    
> with(partitions):  
> 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]

DISCUSSION:  
  This table of the 41 vector partitions of 4 with weight and crank
                    
SEE ALSO: vpcrank, vpw