FUNCTION :  pntOP - Returns true if a partition into odd parts
                

CALLING SEQUENCE :  pntOP(ptn)
                    

PARAMETERS :   ptn   -  partition (list of nonnegative integers)

SYNOPSIS :   
 pntOP(ptn) returns true if the partition ptn is a partition into
 odd parts.   

EXAMPLES :   
> with(combinat):
> read %FUNCS.txt%:
> ptn1:=[1,3,6];
                               ptn1 := [1, 3, 6]
> ptnOP(ptn1);
                                     false
> ptn2:=[1,3,3,5];
                              ptn2 := [1, 3, 3, 5]
> ptnOP(ptn2);
                                      true
> ptns:=partition(9):
> ptns1:=select(ptnOP,ptns);
ptns1 := [[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 3, 3],
    [3, 3, 3], [1, 1, 1, 1, 5], [1, 3, 5], [1, 1, 7], [9]]
> printptns(ptns1);
9
`7 + 1 + 1`
`5 + 3 + 1`
`5 + 1 + 1 + 1 + 1`
`3 + 3 + 3`
`3 + 3 + 1 + 1 + 1`
`3 + 1 + 1 + 1 + 1 + 1 + 1`
`1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1`

DISCUSSION :
The ptn1=[1,3,6] is not a partition into odd parts but the
partition ptn2=[1,3,3,5] is. There are 8 partitions of 9 into
odd parts:
9, 7 + 1 + 1, 5 + 3 + 1, 5 + 1 + 1 + 1 + 1, 3 + 3 + 3,
3 + 3 + 1 + 1 + 1, 3 + 1 + 1 + 1 + 1 + 1 + 1,
and 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1.


SEE ALSO :  ptnDP