A combinatorial introduction to Adinkras

TL;DR

This paper explores the combinatorial structure of Adinkras, graphical tools used in supersymmetry, introducing Latin rectangles as a new way to characterize these graphs and enhance their mathematical understanding.

Contribution

It introduces a novel characterization of Adinkras using Latin rectangles, expanding the combinatorial framework for analyzing supersymmetry-related graphs.

Findings

Adinkras are a special class of 1-factorizations with unique properties.

Latin rectangles effectively characterize Adinkras.

The combinatorial approach aids in solving differential equations in supersymmetry.

Abstract

We survey the combinatorics of the Adinkra, a graphical device for solving differential equations in supersymmetry. These graphs represent an exceptional class of 1-factorizations with further augmentations. As a new feature, we characterize Adinkras using Latin rectangles.