FUNCTION:  partitions[ptnSCHUR] - Schur partitions
 
CALLING SEQUENCE:  ptnSCHUR(ptn)
 
PARAMETERS:    ptn -  partition
 
GLOBAL VARIABLES:  NONE

SYNOPSIS:  
   Returns true if ptn is a partition in which difference between parts
   is at least 3 and such that no two consecutive multiples of 3
   occur as parts
                    
EXAMPLES:  
                    
> with(combinat):
> with(partitions):
> with(qseries):
> ptns:=partition(8):
> ptns1:=select(ptnSCHUR,ptns);
                         ptns1 := [[2, 6], [1, 7], [8]]

> ptns2:=select(ptn-> if convert(modp(ptn,6),set) subset {1,5} then true 
         else false fi, ptns);
           ptns2 := [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 5], [1, 7]]

> nops(ptns), nops(ptns1), nops(ptns2);
                                    22, 3, 3

DISCUSSION:  There are 22 partitions of 8.
             Of these 3 satisfy the condition (listed)
             We also find the partitions of 8 with parts congruent to
             1 or 5 mod 6.
                    
SEE ALSO: PSCHUR