FUNCTION: ListCompo - list of compositions of a given weight

CALLING SEQUENCE:

ListCompo(n)

COMP[ListCompo](n)

PARAMETERS:

n = any non negative integer

SYNOPSIS:

• The ListCompo function gives all compositions of n. A composition of n is list of positive integers, called parts, with sum n.

• When called with one argument, say n, the function returns the list of all compositions of n.

• The following options are available:
  'lg'=l sets the number of parts of each composition.
  'lg'<=l sets the maximal number of parts of each composition.
  'maxouter'=p sets the outermost possible shape of the diagram (composition with possible zeros).
  'allowzeros' compositions may include zeros.
  'nb' returns the number of compositions instead of the list thereof.

• Given a composition comp, convert(comp, `+`) gives its weight.

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

EXAMPLES:

> with(COMP):
> ListCompo(3);
 
                      [[3], [2, 1], [1, 2], [1, 1, 1]]
 
> ListCompo(2, 'allowzeros', 'lg'=3);
 
     [[2, 0, 0], [1, 1, 0], [1, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]]
 
> ListCompo(5, 'maxouter'=[1,0,3], 'allowzeros', 'lg'<=4);
 
  [[1, 0, 3, 1], [1, 0, 2, 2], [1, 0, 1, 3], [1, 0, 0, 4], [0, 0, 3, 2],
 
                 [0, 0, 2, 3], [0, 0, 1, 4], [0, 0, 0, 5]]
 
> ListCompo(20, 'lg'<=10, 'nb');
 
                                     262144