FUNCTION: partitions[ptnRR] - Rogers-Ramanujan partitions
CALLING SEQUENCE: ptnRR(ptn)
PARAMETERS: ptn - partition
GLOBAL VARIABLES: NONE
SYNOPSIS:
Returns true if ptn is a partition in which difference between parts
is at least 2.
EXAMPLES:
> with(combinat):
> with(partitions):
> ptns:=partition(8):
> ptns1:=select(ptnRR,ptns);
ptns1 := [[3, 5], [2, 6], [1, 7], [8]]
> ptns2:=select(ptn-> if convert(modp(ptn,5),set) subset {1,4} then true
else false fi, ptns);
ptns2 := [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 4], [4, 4], [1, 1, 6]]
> nops(ptns), nops(ptns1), nops(ptns2);
22, 4, 4
DISCUSSION: There are 22 partitions of 8.
Of these 4 satisfy the condition (listed)
We also find the partitions of 8 with parts congruent to
1 or 4 mod 5.
SEE ALSO: PRR