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