2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58971We obtain the specialization of monomial symmetric functions on the alphabet (a-b)/(1-q). This gives a remarkable algebraic identity, and four new developments for the Macdonald polynomial associated with a row. The proofs are given in the framework of $λ$-ring theory.25 pages, LaTeX, in French. Enlarged version, with new remarks, misprints corrected, and an Appendix addedCombinatoricstext