Physical Sciences and Mathematics Commons^™

On Powers Of 2 Dividing The Values Of Certain Plane Partition Functions, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T(n) and C(n) are the numbers of such plane partitions in a 2n × 2n × 2nbox, then

ord₂(T(n)) = ord₂(C(n))

for all n >= 1. We also discuss various consequences, along with other results on ord₂(T(n)).