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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Adinkras for mathematicians
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by Yan X. Zhang PDF
Trans. Amer. Math. Soc. 366 (2014), 3325-3355 Request permission


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
  • Received by editor(s): May 11, 2012
  • Received by editor(s) in revised form: November 22, 2012
  • Published electronically: February 6, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3325-3355
  • MSC (2010): Primary 05A99
  • DOI:
  • MathSciNet review: 3180749