Supersymmetry and Combinatorics

TL;DR

This paper explores how a supersymmetric quantum mechanics model provides new insights into the combinatorics of binary necklaces and shift-registers, with implications for algebraic structures like the Witten index.

Contribution

It introduces a novel connection between supersymmetry and combinatorial structures, offering new conjectures and results on binary necklaces and shift-registers.

Findings

Supersymmetry imposes constraints on binary necklaces.

Projection based on Pauli's exclusion principle reveals algebraic structures.

Results generalize the concept of the Witten index.

Abstract

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.