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