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The branching coefficients in the expansion of the elementary symmetricfunction multiplied by a symmetric Macdonald polynomial $P_\kappa(z)$ are knownexplicitly. These formulas generalise the known $r=1$ case of the Pieri-typeformulas for the nonsymmetric Macdonald polynomials $E_\eta(z)$. In this paperwe extend beyond the case $r=1$ for the nonsymmetric Macdonald polynomials,giving the full generalisation of the Pieri-type formulas for symmetricMacdonald polynomials. The decomposition also allows the evaluation of thegeneralised binomial coefficients $\tbinom{\eta }{\nu }_{q,t}$ associated withthe nonsymmetric Macdonald polynomials.

Further Pieri-type formulas for the nonsymmetric Macdonald polynomials