Supersymmetry and Combinatorics

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...

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. Fermi statistics plays a crucial role by projecting out certain states/necklaces by virtue of Pauli's famous exclusion principle. Some of our results can be rephrased in terms of generalizations of the well-...

Combinatorics Enumerative Combinatorics 05

Analytic Combinatorics — Symbolic Combinatorics

This booklet develops in nearly 200 pages the basics of combinatorial enumeration through an approach that revolves around generating functions. The major objects of interest here are words, trees, graphs, and permutations, which surface recurrently in all areas of discrete mathematics. The text presents the core of the theory with chapters on unlabelled enumeration and ordinary generating func...

General covariance and supersymmetry without supersymmetry.

An unusual four-dimensional generally covariant and supersymmetric SU(2) gauge theory is described. The theory has local degrees of freedom, and is invariant under a local (left-handed) chiral supersymmetry, which is half the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the theory reveals the remarkable feature that the local supersymmetry is a consequence of Yang-Mills s...