FUNCTION: ListPartIn - list of partitions contained into a given partition or between two given partitions

CALLING SEQUENCE:

ListPartIn(part)

ListPartIn(part, part_in)

PART[ListPartIn](part)

PART[ListPartIn](part, part_in)

PARAMETERS:

part, part_in = any lists denoting partitions

SYNOPSIS:

• The ListPartIn function gives all partitions contained into the diagram of a given partition. The list is ordered by increasing length.

• Called with a second argument part_in, the function returns the list of all partitions contained into the diagram of part and containing the diagram of part_in.

• The following options are available:
  'weight' = w imposes the weight of partitions.
  'nb' returns the number of partitions instead of the list thereof.

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

EXAMPLES:

> with(PART):
> ListPartIn([3,1]);
 
                 [[], [1], [2], [3], [1, 1], [2, 1], [3, 1]]
 
> ListPartIn([3,2,1], [2,1,1]);
 
                 [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 2, 1]]
 
> ListPartIn([4,3,2], 'weight'=6);
 
               [[4, 2], [3, 3], [4, 1, 1], [3, 2, 1], [2, 2, 2]]
 
> ListPartIn([40,30,15,10,8,7,5,3,1], 'nb');
 
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