Title: Composite fermion basis for M-component Bose gases,
Abstract: 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.