Geodesic
Recurrence formulas for Macdonald polynomials of type $A$
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 1, pp. 113-131.

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Summary: We consider products of two Macdonald polynomials of type $A$, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero component on the $k$th fundamental weight. We give the explicit decomposition of any Macdonald polynomial of type $A$ in terms of this basis.
Keywords: Macdonald polynomials, Pieri formula, multidimensional matrix inverse 
@article{JAC_2010__32_1_a1,
     author = {Lassalle, Michel and Schlosser, Michael J.},
     title = {Recurrence formulas for {Macdonald} polynomials of type $A$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {113--131},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__32_1_a1/}
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Lassalle, Michel; Schlosser, Michael J. Recurrence formulas for Macdonald polynomials of type $A$. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 1, pp. 113-131. http://geodesic.mathdoc.fr/item/JAC_2010__32_1_a1/