  We suggest a general rule for the shift quantum numbers k of the relative
ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes
well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even
rings. Our rule is confirmed by numerical investigations and rigorous proofs
for special cases, including systems with a Haldane gap. Implications for the
total spin quantum number S of relative ground states are discussed as well as
generalizations to the XXZ model.
