Adinkras for mathematicians. Adinkras are graphical tools created for the study of supersymmetry representations. Besides having inherent interest for physicists, the study of Adinkras has already shown connections with coding theory and Clifford algebras. Furthermore, adinkras offer many natural and accessible mathematical problems of combinatorial nature. We present the foundations for a mathematical audience, make new connections to other fields (homological algebra, poset theory, and polytopes), and solve some of these problems. Original results include the enumeration of all hypercube adinkras through dimension 5, the enumeration of odd dashings of Adinkras for any dimension, and a connection between rankings and the chromatic polynomial for certain graphs.
Keywords for this software
References in zbMATH (referenced in 11 articles )
Showing results 1 to 11 of 11.
- Mansour, Toufik; Schork, Matthias: On the differential equation of first and second order in the Zeon algebra (2021)
- Gates, S. James jun.; Hu, Yangrui; Mak, S.-N. Hazel: Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces (2020)
- Mak, S.-N. Hazel; Stiffler, Kory: 4D, (\mathcalN= 1) matter gravitino genomics (2019)
- Marcolli, Matilde; Zolman, Nick: Adinkras, dessins, origami, and supersymmetry spectral triples (2019)
- Gates, S. James (jun.); Guyton, Forrest; Harmalkar, Siddhartha; Kessler, David S.; Korotkikh, Vadim; Meszaros, Victor A.: Adinkras from ordered quartets of (BC_4) Coxeter group elements and regarding 1,358,954,496 matrix elements of the gadget (2017)
- Iga, Kevin; Zhang, Yan X.: Structural theory and classification of 2D Adinkras (2016)
- Calkins, Mathew; Gates, D. E. A.; Gates, S. James jun.; Golding, William M.: Think different: applying the old macintosh mantra to the computability of the SUSY auxiliary field problem (2015)
- Gates, S. James jun.; Hübsch, T.; Stiffler, Kory: Adinkras and SUSY holography: some explicit examples (2014)
- Zhang, Yan X.: Adinkras for mathematicians (2014)
- Zhang, Yan X.: Adinkras for mathematicians (2013)
- Gates, S. James jun.; Hallett, Jared; Parker, James; Rodgers, Vincent G. J.; Stiffler, Kory: 4(D), (\mathcalN= 1) supersymmetry genomics. II (2012)