The combinatorics of adinkras
Author(s)Zhang, Yan, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Mathematics.
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Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and computational nature. In this work, we make a self-contained treatment of the mathematical foundations of adinkras that slightly generalizes the existing literature. Then, we make new connections to other areas including homological algebra, theory of polytopes, Pfaffian orientations, graph coloring, and poset theory. Selected results include the enumeration of odd dashings for all adinkraizable chromotopologies, the notion of Stiefel-Whitney classes for codes and their vanishing conditions, and the enumeration of all Hamming cube adinkras up through dimension 5.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 67-69).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology