Counting 1/8-BPS dual-giants

We count 1/8-BPS states in type IIB string theory on AdS5 x S5 background which carry three independent angular momenta on S5. These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigenstates of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS5 and one nonzero angular momentum on S5 by considering configurations of arbitrary number of giant gravitons that share at least four supersymmetries.