We prove in theorems 2 and 3 that for 1D Bosons with repulsive delta function interaction with any number of components and any Young tableau, the energy per particle as N → ∞ is the same as for spinless Bosons.
The problem of N particles interacting in one dimension by a repulsive delta-function potential is solved, when the wave function $\ensuremath{\psi}$ transforms like any irreducible representation ${R}_{\ensuremath{\psi}}$ of SN for which the Young tableau consists of a finite number of either rows or columns.