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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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

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
  • 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: https://doi.org/10.1090/S0002-9947-2014-06031-5
  • MathSciNet review: 3180749