Composite fermion basis for M-component Bose gases
  The composite fermion (CF) formalism produces wave functions that are not
always linearly independent. This is especially so in the low angular momentum
regime in the lowest Landau level, where a subclass of CF states, known as
simple states, gives a good description of the low energy spectrum. For the
two-component Bose gas, explicit bases avoiding the large number of redundant
states have been found. We generalize one of these bases to the $M$-component
Bose gas and prove its validity. We also show that the numbers of linearly
independent simple states for different values of angular momentum are given by
coefficients of $q$-multinomials.
