2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78169We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating function. It would be interesting to obtain a bijective proof. We present a conjecture generalizing this identity.20 pages, LaTeX, in French. Enlarged version, with a new section added. To appear in Journal of Combinatorial Theory, serie ACombinatoricstext