FUNCTION: partitions[overptnrank] - overpartition rank CALLING SEQUENCE: overptnrank(optn) PARAMETERS: optn - LIST [dptn, ptn] where dptn is a partition into distinct parts and ptn is a partition SYNOPSIS: overptnrank(optn) returns the overpartition rank of the of the overpartition optn EXAMPLES: > with(combinat): > with(partitions): > with(orank): > RT4:=[seq(overptnrank(overptns(4)[k]),k=1..14)]; RT4 := [-3, -1, 0, 1, 3, -3, -1, 1, -1, 0, -1, 1, 1, 3] > seq(nops(select(x->if x=k then true else false fi,RT4)),k=-4..4); 0, 2, 0, 4, 2, 4, 0, 2, 0 > seq(NBAR(abs(k),4),k=-4..4); 0, 2, 0, 4, 2, 4, 0, 2, 0 DISCUSSION: We calculated the 14 overpartitions of 4 and their overpartition ranks. We also confirmed the values of NBAR(m,n) for n = 4. NBAR(m,n) = number of overpartitions of n with overpartition rank m SEE ALSO: overptns, overptncrank