Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry

TL;DR

This paper establishes a novel connection between the classification of supersymmetry representations, graph theory, and error-correcting codes, providing a new framework for understanding supersymmetric structures.

Contribution

It demonstrates that classifying supersymmetry representations can be reduced to problems in graph theory and coding theory, linking these mathematical areas.

Findings

Equivalence between supersymmetry representation classification and graph classification.

Equivalence between supersymmetry representation classification and error-correcting code classification.

Provides a new approach to classify supersymmetry representations using combinatorial and coding theory methods.

Abstract

Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for each topological type. The latter problem being solved by a recursive mechanism that generates all height-assignments within a topology, it remains to classify the former. Herein we show that this problem is equivalent to classifying certain (1) graphs and (2) error-correcting codes.