Supersymmetry and Combinatorics *

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 sub-space. Some of our results can be rephrased in terms of generalizations of the well-known Witten index. In a recent series of papers [1]–[3] two of us have introduced a supersymmetric quantum mechanical matrix model and studied some of its intriguing properties. The model is defined as the N → ∞ limit of a quantum mechanical system whose degrees of freedom are bosonic and fermionic N ×N creation and destruction operator matrices. The model's supersymmetry charges and Hamiltonian are explicitly given by: