 the study of multi-component quantum mixtures with strongly repulsive contact interactions in a one-dimensional harmonic trap reveals that the ground state has the most symmetric spatial wave function allowed by the type of mixture, providing an example of the generalized Liebmattis theorem. Furthermore, the symmetry properties of the mixture are embedded in the large momentum tails of the momentum distribution, which can be evaluated both at infinite repulsion using an exact solution, and at finite interactions using a numerical DMRG approach. An experimental measurement of the tan's contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture. This article was authored by Gene DeKamp, Johannes Junemann, Mathias Albert and others.