  In this paper we give Pfaffian expressions and constant term identities for
the enumeration problems presented by Mills, Robbins and Rumsey
(``Self-complementary totally symmetric plane partitions'' J. Combin. Theory
Ser. A, 42, 277--292), concerning the totally symmetric self-complementary
plane partitions (TSSCPPs). We also present some new conjectures and give
Pfaffian expressions for them.
