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Adinkras are graphical representations of the gauge invariant field components in supersymmetric theories and their orbits under the action of supersymmetry (SUSY) generators in the context of supermultiplets. A discussion is given that…

Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the "gadget" as a function of pairs of adinkras, obtaining some mysterious results for $(n=4, k=1)$ adinkras with computer-aided…

The problem of classifying off-shell representations of the $N$ -extended one-dimensional super Poincar\'e algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as Adinkras. In…

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…

Every finite-dimensional unitary representation of the N-extended worldline supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets…

We continue the development of a theory of off-shell supersymmetric representations analogous to that of compact Lie algebras such as SU(3). For off-shell 4D, N = 1 systems, quark-like representations have been identified [1] in terms of…

Adinkras are highly structured graphs developed to study 1-dimensional supersymmetry algebras. A cyclic ordering of the edge colors of an Adinkra, or rainbow, determines a Riemann surface and a height function on the vertices of the Adinkra…

Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a…

Starting from higher dimensional adinkras constructed with nodes referenced by Dynkin Labels, we define "adynkras." These suggest a computationally direct way to describe the component fields contained within supermultiplets in all…

The problem of classifying off-shell representations of the $N$-extended one-dimensional super Poincar\'{e} algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as {\em…

Applying an efficient pattern-based computational method of generating the so-called 'resonating' algebraic structures results in a broad class of the new Lie (super)algebras. Those structures inherit the AdS base (anti)commutation pattern…

Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplacian matrices. These matrices each have exactly two distinct…

Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain…

Superbubbles are acyclic induced subgraphs of a digraph with single entrance and exit that naturally arise in the context of genome assembly and the analysis of genome alignments in computational biology. These structures can be computed in…

Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit…

Adinkras are graphical gadgets introduced by physicists to study supersymmetry, which can be thought of as the Cayley graphs for supersymmetry algebras. Improving the result of Iga et al., we determine the critical group of an Adinkra given…

Evidence is presented in some examples that an adinkra quantum number, $\chi_{\rm o}$ (arXiv:\ 0902.3830 [hep-th]), seems to play a role with regard to off-shell 4D, $\cal N$ = 2 SUSY similar to the role of color in QCD. The vanishing of…

We consider a class of Poincar\'e superalgebras for which the nested bracket of three supercharges is necessarily zero only in dimensions greater than three. In lower dimensions, we give a precise characterisation of the data which encodes…

For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented.…

We consider some unitary representations of infinite dimensional Lie algebras motivated by string theory on AdS_3. These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first…