Companion problems in quasispin and isospin

We note that the same mathematical results apply to problems involving quasispin and isospin, but the problems per se are different. In the quasispin case, one deals with a system of identical fermions (e.g. neutrons) and address the problem of how many seniority conserving interactions there are. In the isospin case, one deals with a system of both neutrons and protons and the problem in question is the number of neutron-proton pairs with a given total angular momentum. Other companion problems are also discussed.