FUNCTION: partitions[overptncrank] - overpartition crank
CALLING SEQUENCE: overptncrank(optn)
PARAMETERS: optn - list [dptn, ptn]
where dptn is a partition into distinct parts
and ptn is a partition
SYNOPSIS:
overptncrank(optn) returns the overpartition crank of the
overpartition optn
EXAMPLES:
> with(combinat):
> with(partitions):
> with(ocrank):
> CT4:=[seq(overptncrank(overptns(4)[k]),k=1..14)];
CT4 := [-4, -2, 2, 0, 4, -3, 0, 3, -2, 2, -1, -1, 1, 1]
> seq(nops(select(x->if x=k then true else false fi,CT4)),k=-4..4);
1, 1, 2, 2, 2, 2, 2, 1, 1
> seq(MBAR(abs(k),4),k=-4..4);
1, 1, 2, 2, 2, 2, 2, 1, 1
DISCUSSION:
We calculated the 14 overpartitions of 4 and their
overpartition cranks. We also confirmed the values
of MBAR(m,n) for n = 4.
MBAR(m,n) = number of overpartitions of n with overpartition crank m
SEE ALSO: overptns, overptncrank