Structural Theory of 2-d Adinkras

Abstract

Adinkras are combinatorial objects developed to study 1-dimensional supersymmetry representations. Recently, 2-d Adinkras have been developed to study 2-dimensional supersymmetry. In this paper, we classify all 2-d Adinkras, confirming a conjecture of T. H\"ubsch. Along the way, we obtain other structural results, including a simple characterization of H\"ubsch's even-split doubly even code.