FUNCTION: ListPart - list of partitions of a given weight

CALLING SEQUENCE:

ListPart(n)

PART[ListPart](n)

PARAMETERS:

n = any non negative integer

SYNOPSIS:

• The ListPart function gives all partitions of n. A partition of n is a weakly decreasing list of positive integers, called parts, with sum n.

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

• The following options are available:
  'maxlg' = l sets the maximal number of parts of each partition.
  'maxpart' = p enumerates only the partitions pa such that pa[1] <= p[1], ..., pa[nops(p)] <= p[nops(p)].
  'regular' = m only m-regular partitions are listed (no part is repeated strictly more than m times).
  'nb' returns the number of partitions instead of the list thereof.

• Given a partition part, convert(part,`+`) gives its weight.

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

EXAMPLES:

> with(PART):
> ListPart(4);
 
              [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]
 
> ListPart(5, 'maxlg'=3);
 
                [[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1]]
 
> ListPart(5, 'maxpart'=[3,2], 'maxlg'=3);
                         [[3, 2], [3, 1, 1], [2, 2, 1]]
 
> ListPart(100, 'nb');
                                   190569292