FUNCTION: ListSkewPart - list of partitions of a given weight, optionnally
constrained
CALLING SEQUENCE:
- ListSkewPart(n)
- PART[ListSkewPart](n)
-
PARAMETERS:
- n = any non negative integer
SYNOPSIS:
- The ListSkewPart function gives all skew partitions of n.
- 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).
- When called with one argument, say n, the function returns the list of
all skew partitions of n.
- You may set some constraints on skew partitions by using one or several
options:
- 'maxlg'=l majorates the length of skew partitions,
- '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 partitions instead
of the list thereof.
- The outer partition corresponds to the outer shape of the skew parti-
tion and the inner partition corresponds to the inner shape of the skew
partition.
- Given a partition part , convert(part,`+`) gives its weight.
- Whenever there is a conflict between the function name ListSkewPart and
another name used in the same session, use the long form
PART['ListSkewPart'].
EXAMPLES:
> with(PART):
> ListSkewPart(2);
[[[2], []], [[2, 1], [1]], [[1, 1], []]]
> ListSkewPart(3, 'mininner'=[1], 'maxouter'=[3,1,1]);
[[[3, 1], [1]], [[2, 1, 1], [1]]]
> ListSkewPart(3, 'maxinner'=[1], 'minouter'=[3]);
[[[3], []], [[3, 1], [1]]]
> ListSkewPart(10, 'maxlg'=5, 'nb');
5309
SEE ALSO: SkewPart2Mat ListPart ListPartIn
