A unified enumeration of 1-dimension garden algebras and valise Adinkras

Abstract

In the study of supersymmetry in one dimension, various works enumerate sets of generators of garden algebras GR($d,N$) (and equivalently, valise Adinkras) for special cases $N=d=4$ and $N=d=8$, using group-theoretic methods and computer computation. We complement this work by enumerating the objects for arbitrary $N$ and $d$ via a formula in a streamlined manner.