FUNCTION: CompPart - compare two partitions

CALLING SEQUENCE:

CompPart(part1, part2)

CompPart(part1, part2, kind)

PART[CompPart](part1, part2)

PART[CompPart](part1, part2, kind)

PARAMETERS:

part1, part2 = any partitions

kind = 'natural', 'lexic', 'cixel'

SYNOPSIS:

• The CompPart function compares two partitions for the given ordering.

• The considered ordering is given by the second argument kind:
  'natural' : part1 >= part2 if sum_part1<=sum_part2 for the lexicographic ordering (sum_I=[I[1], I[1]+I[2], I[1]+I[2]+I[3], ...]).
  'lexic' : part1>=part2 for the lexicographic ordering.
  'cixel' : part1>=part2 for the inverse lexicographic ordering.

• Without a third argument, the comparison is assumed to be natural.

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

EXAMPLES:

> with(PART):
> CompPart([3,2,1], [3,2,1,1], 'cixel');
 
                                      true
 
> CompPart([3,2,1], [3,2,1,1], 'lexic');
 
                                     false
 
> CompPart([3,2,1], [3,2,1,1]);
 
                                      true