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Adinkras for Mathematicians

Abstract : $\textit{Adinkras}$ 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.
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https://hal.inria.fr/hal-01229733
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Submitted on : Tuesday, November 17, 2015 - 10:20:46 AM
Last modification on : Wednesday, June 26, 2019 - 2:48:03 PM
Long-term archiving on: : Friday, April 28, 2017 - 2:47:46 PM

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Yan X. Zhang. Adinkras for Mathematicians. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.457-468. ⟨hal-01229733⟩

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