  The SU(n) symmetric antiferromagnetic finite chain with the fundamental
representation and nearest-neighbor interaction is studied. A partial ordering
between the lowest energy levels e(Y) in multiplet sectors corresponding to
different Young tableaux Y is established for the chains with arbitrary
site-dependent couplings.
  For the open chains it is proved that e(Y1)>e(Y2) if Y2 may be obtained from
Y1 moving down some of its boxes. In particular, the ground state of the chain
belongs to the antisymmetric multiplet sector. For the rings the same condition
is fulfilled if, in addition, all rows of Y2 are of even or odd length. The
ground state is SU(n) singlet if the chain's length is a multiple of n both for
open and periodic chains.
  The results generalize the well known Lieb-Mattis theorem to chains with
higher symmetries.
