Even-denominator quantum Hall effect and the hierarchy of spin-singletv=2(2q+1)fluids

I point out a hierarchy connection between the even-denominator filling-fraction quantum Hall effect and the spin-singlet $v=\frac{2}{\mathrm{}(2q+1)\mathrm{}}$ Halperin states. Hierarchical construction produces spin-singlet states at all (even and odd) primary filling fractions as well as spin-singlet and partially polarized ones at secondary filling fractions. The possible relation of some of these states to recently proposed ones, such as the hollow-core model, is briefly discussed.