FUNCTION:  partitions[vpcrank] - vector partition crank
 
CALLING SEQUENCE:  vpcrank(vptn)
 
PARAMETERS:    vptn - vector partition [dptn, ptn, ptn]
 
GLOBAL VARIABLES: NONE

SYNOPSIS:  
    crank of vector ptn [P1,P2,P3] is #(P2)-#(P3)
                    
EXAMPLES:  
                    
> with(partitions):  
> V3:=vecptns(3);
V3 := [[[], [], [1, 1, 1]], [[], [], [1, 2]], [[], [], [3]], [[], [1], [1, 1]],
    [[], [1], [2]], [[], [1, 1], [1]], [[], [2], [1]], [[], [1, 1, 1], []],
    [[], [1, 2], []], [[], [3], []], [[1], [], [1, 1]], [[1], [], [2]],
    [[1], [1], [1]], [[1], [1, 1], []], [[1], [2], []], [[2], [], [1]],
    [[2], [1], []], [[1, 2], [], []], [[3], [], []]]

> nops(V3);
                                       19

> [seq(vpcrank(vp), vp in V3)];
        [-3, -2, -1, -1, 0, 1, 0, 3, 2, 1, -2, -1, 0, 2, 1, -1, 1, 0, 0]

DISCUSSION: We calculate the vector partition crank of the 19 
            vector partitions of 3
                    
SEE ALSO: vecptns, vecptnsC, vpw