  We address the problem, previously considered by Ginocchio and Haxton (G-H),
of the number of states for three identical particles in a single j-shell with
angular momentum J=j. G-H solved this problem in the context of the quantum
Hall effect. We address it in a more direct way. We also consider the case
J=j+1 to show that our method is more general, and we show how to take care of
added complications for a system of five identical particles.
