  We show how a recently proposed supersymmetric quantum mechanics model leads
to non-trivial results/conjectures on the combinatorics of binary necklaces and
linear-feedback shift-registers. Pauli's exclusion principle plays a crucial
role: by projecting out certain states/necklaces, it allows to represent the
supersymmetry algebra in the resulting subspace. Some of our results can be
rephrased in terms of generalizations of the well-known Witten index.
