2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92376We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive tables of marginal inequalities, including arrays up to 4 qubits. In the second part of the paper we pursue another approach based on reduction of the problem to representation theory of the symmetric group.AMS-LaTeX version 2.08, 47 pagesQuantum Physicstext