FUNCTION: ListSkewDiag - list of skew diagrams

CALLING SEQUENCE:

ListSkewDiag(n)

PART[ListSkewDiag](n)

PARAMETERS:

n = any non negative integer

SYNOPSIS:

• The ListSkewDiag function gives all skew diagrams of n. Skew diagrams are special cases of skew partitions.

• A skew partition of n is a list of two partitions part1 and part2 such that part1 is greater than part2 (with respect to inclusion of diagrams) and n equals (weight of part1) minus (weight of part2).

• A skew diagram is a skew partition without empty rows or columns.

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

• You may set some constraints on skew diagrams by using one or several options:
  'maxlg'=l majorates the length of skew diagrams,
  'mininner'= p imposes the minimal inner partition,
  'maxinner'= p imposes the maximal inner partition,
  'minouter'= p imposes the minimal outer partition,
  'maxouter'= p imposes the maximal outer partition,
  'nb' returns the number of skew diagrams instead of the list thereof.

• The outer partition corresponds to the outer shape of the skew diagram and the inner partition corresponds to the inner shape of the skew diagram.

• Given a skew diagram skd, convert(op(1,skd),`+`)-convert(op(2,skd),`+`) gives its weight.

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

EXAMPLES:

> with(PART):
> ListSkewDiag(2);
 
                    [[[2], []], [[2, 1], [1]], [[1, 1], []]]
 
> ListSkewDiag(3, 'mininner'=[1], 'maxouter'=[3,1,1]);
 
                       [[[3, 1], [1]], [[2, 1, 1], [1]]]
 
> ListSkewDiag(3, 'maxinner'=[1], 'minouter'=[3]);
 
                          [[[3], []], [[3, 1], [1]]]
 
> ListSkewDiag(10, 'maxlg'=5, 'nb');
 
                                      5309