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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Adinkras for mathematicians


Author: Yan X. Zhang
Journal: Trans. Amer. Math. Soc. 366 (2014), 3325-3355
MSC (2010): Primary 05A99
Published electronically: February 6, 2014
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Abstract: Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown non-trivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and computational nature. We survey these topics for a mathematical audience, make new connections to other areas (homological algebra and poset theory), and solve some of these said problems, including the enumeration of all hypercube adinkras up through dimension $ 5$ and the enumeration of odd dashings of adinkras for any dimension.


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Additional Information

Yan X. Zhang
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06031-5
PII: S 0002-9947(2014)06031-5
Received by editor(s): May 11, 2012
Received by editor(s) in revised form: November 22, 2012
Published electronically: February 6, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.