FUNCTION: SplitPart - split a partition into several ones

CALLING SEQUENCE:

SplitPart(part)

PART[SplitPart](part)

SplitPart(part,n)

PART[SplitPart](part,n)

PARAMETERS:

part = a partition

n = any positive integer

SYNOPSIS:

• The SplitPart function returns the set of ways of splitting the partition part into two partitions.

• Called with a second argument n, the partition is splitted into n partitions.

• Whenever there is a conflict between the function name SplitPart and another name used in the same session, use the long form PART['SplitPart'].

EXAMPLES:

> with(PART):
> SplitPart([4,2,1]);
 
      {[[2], [4, 1]], [[4], [2, 1]], [[], [4, 2, 1]], [[4, 2, 1], []],
 
          [[2, 1], [4]], [[4, 1], [2]], [[1], [4, 2]], [[4, 2], [1]]}
 
> r := SplitPart([2,1], 3);
 
 r := {[[2, 1], [], []], [[1], [2], []], [[1], [], [2]], [[2], [1], []],
 
        [[], [2, 1], []], [[], [1], [2]], [[2], [], [1]], [[], [2], [1]],
 
        [[], [], [2, 1]]}
 
> map(proc(spt) sort(map(op, spt), proc(x,y) evalb(x>=y) end) end, r);
 
                                 {[2, 1]}