swMATH ID: 9383 Software Authors: Zhang, Yan X. Description: 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. Homepage: http://www.ams.org/journals/tran/2014-366-06/S0002-9947-2014-06031-5/home.html Keywords: supersymmetry; representation theory; Clifford algebras; codes; topology Related Software: LieART; HEPTHools; Adinkra.m; Mathematica; CliffMath; adynkra; Susyno; GitHub Cited in: 27 Publications
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### Cited by 49 Authors

 11 Gates, Sylvester James jun. 5 Iga, Kevin M. 5 Stiffler, Kory 3 Hübsch, Tristan 3 Landweber, Gregory D. 3 Mak, S.-N. Hazel 2 Doran, Charles F. 2 Faux, Michael G. 2 Gates, Delilah E. A. 2 Hu, Yangrui 1 Bellucci, Stefano 1 Calkins, Mathew 1 Douglas, Brendan L. 1 Friend, Isaac 1 Fujimoto, Yukihiro 1 Golding, William M. 1 Grover, Tyler 1 Guyton, Forrest 1 Hallett, Jared 1 Harmalkar, Siddhartha 1 Hasegawa, Kouhei 1 James Gates, S. jun. 1 Kessler, David S. 1 Korotkikh, Vadim 1 Kostiuk, Jordan 1 Koutrolikos, Konstantinos 1 Krivonos, Sergey 1 Mansour, Toufik 1 Marcolli, Matilde 1 Meszaros, Victor A. 1 Miller-Dickson, Miles David 1 Mondal, Benedict A. 1 Nishiwaki, Kenji 1 Oskoui, Amir 1 Parker, James R. 1 Pavšič, Matej 1 Regmi, Shirash 1 Rodgers, Vincent G. J. 1 Ross, Ethan 1 Sakamoto, Makoto 1 Schork, Matthias 1 Segler, B. L. 1 Shetty, Rajath 1 Smilga, Andrei V. 1 Sutulin, Anton 1 Tatsumi, Kentaro 1 Ueba, Inori 1 Wang, Jingbo B. 1 Zolman, Nick
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### Cited in 12 Serials

 11 Journal of High Energy Physics 2 Advances in Applied Clifford Algebras 2 Advances in Mathematical Physics 2 Symmetry 2 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 1 International Journal of Modern Physics A 1 Transactions of the American Mathematical Society 1 Algebras and Representation Theory 1 Foundations of Physics 1 Journal of Physics A: Mathematical and Theoretical 1 Advances in High Energy Physics 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications
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### Cited in 16 Fields

 24 Quantum theory (81-XX) 8 Combinatorics (05-XX) 7 Relativity and gravitational theory (83-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 3 Associative rings and algebras (16-XX) 3 Group theory and generalizations (20-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Differential geometry (53-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX)